Подчеркнем, что канонические признаки оправляются через исходные без перехода к дополнениям. О связи между исходными и каноническими признаками говорит также.
2.6.2 Теорема
Существует такой базис классов порожденной толерантности, что каждый из классов этого базиса содержит некоторое множество
. Доказательство. По определению толерантности в
![](data:image/png;base64,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)
для всякого
![](data:image/png;base64,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)
любая пара
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
толерантна. Значит,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
есть предкласс. Тогда по лемме 2.3.2 получается существует класс
![](data:image/png;base64,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)
. Выберем для каждого
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
один из классов
![](data:image/png;base64,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)
. Очевидно, выбранная совокупность классов удовлетворяет условию 1) из определения 1.4.1. Значит, она содержит некоторый базис
![](data:image/png;base64,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)
.
Следствие. Когда
![](data:image/png;base64,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)
конечно, то существует базис классов толерантности, число классов в котором не превышает количества исходных признаков.
Рассмотрим исходную карту
![](data:image/png;base64,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)
и полученную из нее каноническую карту
![](data:image/png;base64,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)
, где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAXCAYAAAD+4+QTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD2SURBVEjHY2hsbGSgNWYYtWRoWBJlzLCQgYHhPwzLuuUU4xMn2yc5brLFDAyybzzy6g2JESfLErCrjaMWEitOsiX19bGSxgwMd42jG3yIESfLkoZoYx8GBuO7sfX1ksSIUyXiUTCJQYXVko6ONB4PGYY96CmH3KDCakl9noehLIPsTfTUAwkq0lIVTkvASVTGY09aRwcPMeKIZI07/2BNVbiCClfmAwexrOxKkC9Bao0YjHYjJw6croFFMCFXwoNY1mMlyJfgYEXzMVXKJkh84U59VLEElORhqQ6ZTTVLwPEl5z4LFDyw5E9VS2AJglBmHa0ZScIAuB5EH3vCdoMAAAAASUVORK5CYII=)
– базис. Как уже было отмечено, отношения толерантности, издаваемые на множестве обьектов
![](data:image/png;base64,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)
обеими картами, совпадают.
Несколько иначе обстоит дело с отношением эквивалентности
![](data:image/png;base64,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)
, задаваемым на
![](data:image/png;base64,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)
с помощью определения, приведенного в начале параграфа. Пусть
![](data:image/png;base64,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)
– отношение эквивалентности, заданное исходным множеством признаков
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAQCAYAAADwMZRfAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABtSURBVDjLY2hsbGSgFDNQ1ZAcN9liBgaG/0RjGY89aR0dPBguqa+PlTRmYLgr65ZTjM1GXPIoijo60ng8ZBj2EDLEOLrBZ9QQEgyZOHEim4c8Q5ysS54VNkPKy9N4gYbkm8fWq9EusY0aQl1DAIBWioqiziu6AAAAAElFTkSuQmCC)
, а
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACpSURBVDjLY2hsbGQgFTMMUU0dHWk8HjIMexgYGP4zMMi+8cirN8SrqT7Pw1CWQfYmTGGOm2wxg3HUQpya6utjJY0YZE8hm9wQbezDIOOxJ62jgwerJnRTCWrCZgsIRxkzLJR1yynG6jywLWCPY2Lj6AYfDE2w0EI2EZvTUDSBnGbMwHAX2URcBpEUajidB7MJrIHB+G5sfb0k3hQBUQj1PFqwD4dUjg8DAJCAZV8o8UMtAAAAAElFTkSuQmCC)
– отношение эквивалентности, заданное по . Как показывает пример на рис. 1, отношения
![](data:image/png;base64,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)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACpSURBVDjLY2hsbGQgFTMMUU0dHWk8HjIMexgYGP4zMMi+8cirN8SrqT7Pw1CWQfYmTGGOm2wxg3HUQpya6utjJY0YZE8hm9wQbezDIOOxJ62jgwerJnRTCWrCZgsIRxkzLJR1yynG6jywLWCPY2Lj6AYfDE2w0EI2EZvTUDSBnGbMwHAX2URcBpEUajidB7MJrIHB+G5sfb0k3hQBUQj1PFqwD4dUjg8DAJCAZV8o8UMtAAAAAElFTkSuQmCC)
могут и не совпадать. В общем, случае справедлива
2.6.3 Теорема
Если выполнено соотношение:
, то выполнено и соотношение
, т.е.
. Доказательство. Если
![](data:image/png;base64,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)
, то совокупности исходных признаков
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACMAAAAVCAYAAADM+lfpAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAF6SURBVEjH7ZY9boNAEIXnAPYBLLEp08Payg0whZUopUGkiqgsGhco1ZqOJhdI5y45Q3wC3yCFb+A7JBnwkLU1wHpFYUUutoDZn2/evFmAPM/hUsbFgPwvGKXikQfeZ6zUqI951iCrSM4A5K7rgBooDVwB4itIldsrjGmmPJC3bVrXsgj2wl8sKwXgG4eMVjOMhxLWGLNJZOGLJchwbQRTTj7IX0KJ4CMpigG9n6u564HYcnL/gYs9xet3TrDBfdrUafUBApAadc3v5UuXVyh7TgUssQTY0b4sTFEkg8CBDcmPz9Mb+UaHEujD1Cm6YPQyc35DGC7W6PbyWYavFCef6GVsgqHEuOytYPQS6eUzaenUl8/jsXjnjGpUJpqEG+glOlWiamvewASOWevmR7gjxU0MTLWmVsbBycm1dgX9u+agBpXqdI+zWpsO42Q8vvSa1bG9LO2/NwbXu6lXmmHiu1uQ0aPJAVmWDCcweUqybNjHvOv/zBXm3PEDyU0qi2giExMAAAAASUVORK5CYII=)
и
![](data:image/png;base64,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)
, выполненных для
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADFSURBVDjLY2hsbGQgFTMMjCYgYARiZihmRBVbxYRVU0OssTdQwR9GBtnXLlnVRv+BGuojjX1BYgyy7rvSOjp4cDovz0O2iMEoYlGOm2wxg3HUfKL8VJ/nYSjLwPBa1i2nmOiAKC9P4/WQYdhjHFnvS5QmkMfz3IxTTExklwOdthAk9h8SGIwYmqASzCCPy3pkFYGdKOu+MjQtjR9kiEdxgwGGpjw3+TCgpv0MxtGVIH5HRzmnhyxDL0hM3i0vbBCkCJpqAgCV4QwqbGm0yAAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACeSURBVDjLY2hsbGQgFzMMHs1RxgwLGRgY/jPIeOxJ6+jgAYk1RBv7IPPx2gxWzGB8N7a+XhLE7+hI43EzdqslSnN9noehLIPsTY+8ekMwvz5W0s0tL4woP4MUGzMw3DWObvAB8fPc3MJgriBJM8gVxm55KUSHNsiPHjIMe2Q9PXuM5dxnofuVgOZyTg9Zhl5goC0DOld4CCSSUc34MQCZjXm1ne2W5AAAAABJRU5ErkJggg==)
, совпадают. Из теоремы 2.6.1 вытекает, что для каждого класса толерантности
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGQgFTMMjKb/DAyMDAwMLFDMiCoWyoxVU32ssTdQwW9GRtlXLln1xqtWMTBVR5r6gsQYZD12pnV08OB0Xp6HbBGDUcSiLDf5YgaTqHlE+amh2MNAloHhtaxHXhHRAdFRnsbrIcOwxziy3pcoTSCP57kZp5iYyC5jMI5aCBJbxcDABAsYFE0gT4NCCeRxWY+cQpAT5WTdV4ampQmADPEobjDA0JTnJh8G1LSfwTi6EuzEjnJOD1mGXpCYvFte2CBIETTVBADjCA9Na/gVjgAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACeSURBVDjLY2hsbGQgFzMMHs1RxgwLGRgY/jPIeOxJ6+jgAYk1RBv7IPPx2gxWzGB8N7a+XhLE7+hI43EzdqslSnN9noehLIPsTY+8ekMwvz5W0s0tL4woP4MUGzMw3DWObvAB8fPc3MJgriBJM8gVxm55KUSHNsiPHjIMe2Q9PXuM5dxnofuVgOZyTg9Zhl5goC0DOld4CCSSUc34MQCZjXm1ne2W5AAAAABJRU5ErkJggg==)
одновременно содержатся или не содержатся в нем. Таким образом,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGQgFTMMjKb/DAyMDAwMLFDMiCoWyoxVU32ssTdQwW9GRtlXLln1xqtWMTBVR5r6gsQYZD12pnV08OB0Xp6HbBGDUcSiLDf5YgaTqHlE+amh2MNAloHhtaxHXhHRAdFRnsbrIcOwxziy3pcoTSCP57kZp5iYyC5jMI5aCBJbxcDABAsYFE0gT4NCCeRxWY+cQpAT5WTdV4ampQmADPEobjDA0JTnJh8G1LSfwTi6EuzEjnJOD1mGXpCYvFte2CBIETTVBADjCA9Na/gVjgAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACeSURBVDjLY2hsbGQgFzMMHs1RxgwLGRgY/jPIeOxJ6+jgAYk1RBv7IPPx2gxWzGB8N7a+XhLE7+hI43EzdqslSnN9noehLIPsTY+8ekMwvz5W0s0tL4woP4MUGzMw3DWObvAB8fPc3MJgriBJM8gVxm55KUSHNsiPHjIMe2Q9PXuM5dxnofuVgOZyTg9Zhl5goC0DOld4CCSSUc34MQCZjXm1ne2W5AAAAABJRU5ErkJggg==)
имеют одинаковые наборы канонических признаков, т.е.
![](data:image/png;base64,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)
. Теорема доказана.
Следующая теорема, принадлежащая С.М. Якубович, дает условия того, что некоторое множество является классом толерантности, т.е. того, что некоторый признак является каноническим.
2.6.4 Теорема
Пусть имеется карта
. Для, того чтобы элемент покрытия
являлся классом порожденной толерантности
, необходимо и достаточно, чтобы для любого подмножества
, из
следоаало бы
. Доказательство. Сначала предположим, что множество
![](data:image/png;base64,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)
не является классом толерантности. Так как
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
является предклассом, то единственная причина, по которой
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
может не быть классом, состоит в том, что существует
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABUSURBVCjPY2hsbGQgFTMMjKaOjjQeDxmGPQwMDP8RWPaNR169IU5N9XmRqpF59aowfpQxw0Lj6AYfop2HSwNOTfg0YNUUbcxQaRzZYDkIg3zwaQIA4Sb6kacYFMwAAAAASUVORK5CYII=)
, не входящий в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
и толерантный ко всем элементам
![](data:image/png;base64,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)
. Значит, для всякого
![](data:image/png;base64,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)
существует множество
![](data:image/png;base64,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)
, содержащее
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADOSURBVDjLY2hsbGQgFTMMjKb/DAyMDAwMLFDMiCoWyoxVU32ssTdQwW9GRtlXLln1xqtWMTBVR5r6gsQYZD12pnV08OB0Xp6HbBGDUcSiLDf5YgaTqHlE+amh2MNAloHhtaxHXhHRAdFRnsbrIcOwxziy3pcoTSCP57kZp5iYyC5jMI5aCBJbxcDABAsYFE0gT4NCCeRxWY+cQpAT5WTdV4ampQmADPEobjDA0JTnJh8G1LSfwTi6EuzEjnJOD1mGXpCYvFte2CBIETTVBADjCA9Na/gVjgAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABUSURBVCjPY2hsbGQgFTMMjKaOjjQeDxmGPQwMDP8RWPaNR169IU5N9XmRqpF59aowfpQxw0Lj6AYfop2HSwNOTfg0YNUUbcxQaRzZYDkIg3zwaQIA4Sb6kacYFMwAAAAASUVORK5CYII=)
. Таким образом, множества
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAYCAYAAAD6S912AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVEjHY2hsbGSgJmYYNZA2BkYZMyxkYGD4j4KNoxZS5MIcN9liBgbju7H19ZL19bGSxgwMd4kxFKcE2JVQAzo60ng8ZBj2MMh47Enr6OAh2UCYi4yjG3xQDCTXhQ3Rxj4w7yLCFMEn2UBI+CEiBOZSsiIF5j1Zt5xisPfzPAxlGRjewPgkGwgxQPamR169IWoyItPLYO8ixSYpMYxhICx2kb0HS+Qkexk9IhBY9g2y95HTKHpqoCgvR3vI1ssaR/VSrXDIczNOQXc52QaCwtpDVnYltvRJumHgZGV0KrI+0hA9AkdLbOpgAHiTvUPQ0hf8AAAAAElFTkSuQmCC)
образуют покрытие множества
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
. Но все
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAYCAYAAAD6S912AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADrSURBVEjHY2hsbGSgJmYYNZA2BkYZMyxkYGD4j4KNoxZS5MIcN9liBgbju7H19ZL19bGSxgwMd4kxFKcE2JVQAzo60ng8ZBj2MMh47Enr6OAh2UCYi4yjG3xQDCTXhQ3Rxj4w7yLCFMEn2UBI+CEiBOZSsiIF5j1Zt5xisPfzPAxlGRjewPgkGwgxQPamR169IWoyItPLYO8ixSYpMYxhICx2kb0HS+Qkexk9IhBY9g2y95HTKHpqoCgvR3vI1ssaR/VSrXDIczNOQXc52QaCwtpDVnYltvRJumHgZGV0KrI+0hA9AkdLbOpgAHiTvUPQ0hf8AAAAAElFTkSuQmCC)
содержат элемент
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABUSURBVCjPY2hsbGQgFTMMjKaOjjQeDxmGPQwMDP8RWPaNR169IU5N9XmRqpF59aowfpQxw0Lj6AYfop2HSwNOTfg0YNUUbcxQaRzZYDkIg3zwaQIA4Sb6kacYFMwAAAAASUVORK5CYII=)
, не входящий в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
. Следовательно, пересечение
![](data:image/png;base64,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)
не содержится в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
. Итак, мы доказали достаточность условия, указанною в теореме 2.6.4. Докажем теперь необходимость. Пусть существует такое подмножество
![](data:image/png;base64,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)
, что
![](data:image/png;base64,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)
, но
![](data:image/png;base64,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)
. Значит, существует элемент
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAANCAYAAABy6+R8AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABUSURBVCjPY2hsbGQgFTMMjKaOjjQeDxmGPQwMDP8RWPaNR169IU5N9XmRqpF59aowfpQxw0Lj6AYfop2HSwNOTfg0YNUUbcxQaRzZYDkIg3zwaQIA4Sb6kacYFMwAAAAASUVORK5CYII=)
, не входящий в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
, но входящий во все
![](data:image/png;base64,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)
. Этот элемент толерантен ко всем
![](data:image/png;base64,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)
. Значит,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABAAAAARCAYAAADUryzEAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACsSURBVDjLY2hsbGSgBDMMLQPq8zwMjd3yUsgyoKMjjcdDhmGPcXSDD1kGRBkzLGRgYPhPlgEN0cY+xm5utbIMsjc98uoNSTIA5G9Z46hekCEMDMZ3Y+vrJYk2AORvN2O32rSODh6yDID5G45lPPaADCPKALC/kQIMbBixBsD8jeEa46iFBBMS2K9oNsHSgKxbTjFOA+rrYyWNGRjuwvwLUwwJPNzhMMQyEzYMAA2tjN4Ij00uAAAAAElFTkSuQmCC)
не является максимальным предклассом, т.е. не является классом толерантности. Теорема доказана.
Рассмотрим еще так называемые сопряженные и производные пространства толерантности.
Пусть
![](data:image/png;base64,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)
– произвольное пространство толерантности, и пусть
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAYCAYAAAARfGZ1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACwSURBVEjHY2hsbGSgFWYYNXzgDM9xky1mYGD4TzSW8diT1tHBQ7TL6+tjJY0ZGO7KuuUUY1NMSB6v4R0daTweMgx7CBluHN3gM2r4qOHkGQ7LI+j6SEvneR6GsgwMb5ANB4sZR/WC2FHGsr0eefWGROVQmCEwH6HKG9+Nra+XBOmDqWuINvZBdhjF5Ueem3EKzLUgXxi75aVQzXCaupyoMKcERxkzLCSYWkZrIroYDgBJWSUaJjdq1AAAAABJRU5ErkJggg==)
– некоторая совокупность классов толерантности. Множество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAYCAYAAAARfGZ1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACwSURBVEjHY2hsbGSgFWYYNXzgDM9xky1mYGD4TzSW8diT1tHBQ7TL6+tjJY0ZGO7KuuUUY1NMSB6v4R0daTweMgx7CBluHN3gM2r4qOHkGQ7LI+j6SEvneR6GsgwMb5ANB4sZR/WC2FHGsr0eefWGROVQmCEwH6HKG9+Nra+XBOmDqWuINvZBdhjF5Ueem3EKzLUgXxi75aVQzXCaupyoMKcERxkzLCSYWkZrIroYDgBJWSUaJjdq1AAAAABJRU5ErkJggg==)
естественным образом превращается в пространство толерантности
![](data:image/png;base64,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)
при помощи следующего определения:
![](data:image/png;base64,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)
, если
![](data:image/png;base64,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)
.
Определение. Если
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAAYCAYAAAARfGZ1AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADoSURBVEjHY2hsbGSgFWYYNXxwGB5lzLCQgYHhPwzLuuUU4xMn2eU5brLFDAyybzzy6g2JESfJcLArjaMWEitOtOH19bGSxgwMd42jG3yIESfJ8IZoYx8GBuO7sfX1ksSIUxShKJjIIMFqeEdHGo+HDMMe9JRAapBgNbw+z8NQlkH2JnpqgAQJcakEp+HgpCbjsSeto4OHGHFE8sRM91hTCa4gwZZpwD41juqFxJVsL7LPMGxHjzh0cXQLQPKweAAFHbI8xeVHnptxCsy1IF8Yu+WlUM1wmrqcqDCnBMMyHd7UMloT0cVwAK8xJSA2X88kAAAAAElFTkSuQmCC)
совпадает с множеством
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABMAAAARCAYAAAA/mJfHAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADaSURBVDjL7ZM9CsIwHMVfdPYAleYManKFIgE/NgctXR1EMlShg0jak/gx9gxeRLAn8AqKppPF2phBnRze8oP84L3wR5Ik+FTwdVkK1ADUH7kREzfKJhwbAlz1g5vOlYpZaOJva867dAnQs1jEbRtulE0Y9uD+1pZXyqIoaDKQjAdxz4YbZWrMBwDLRlK6xcHX484Q4KdAKcdapofeASQf+lIMyYevqPhSFkXThnBxoEKG5YrIuB/3rWWrmcco6FFI1SlX17/4xI0y6TkUjtcapWndhv/2nP4yY+6iUcRN50MmCwAAAABJRU5ErkJggg==)
всех классов, то пространство
![](data:image/png;base64,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)
называется
сопряженным к
![](data:image/png;base64,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)
и обозначается
![](data:image/png;base64,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)
(таким образом,
![](data:image/png;base64,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)
).