Рассмотрим несколько примеров.
В пространстве
![](data:image/png;base64,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)
элемент
![](data:image/png;base64,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)
, содержащий все числа, толерантен ко всем элементам и, стало быть, входит во все классы толерантности. Значит, в пространствe
![](data:image/png;base64,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)
– полное отношение.
На рис. 4 изображен циклический граф из 7 вершин. Классами толерантности являются "ребра", а толерантны классы, соответствующие смежным ребрам. Ясно, что для линейного графа из
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgFTMMIU319bGSxgwMdxkYGP7LuuUUE20TSKMRg+wpj7x6Q+I15XkYysp6rEzr6OAhWlOOm2wxg3HUQqL91NGRxuMhw7DHOLrBB2wjA8MbkP/Q/YjpNAajU7H19ZLgQDGOridoE8xpyJoJaooyZlgIcw4Dg/FdgpqQgxpik+xNXMEOZzREG/swyHjsAQU1LEBAngezPaKTsWoCOQ05hMD+AztT9g26jUMplROLAcI8Z5L9Aa5bAAAAAElFTkSuQmCC)
вершин сопряженным является линейный граф из
![](data:image/png;base64,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)
вершин.
На рис. 5 изображен циклический граф. Сопряженным к нему будет циклический граф из того же числа верин (если количество вершин исходного графа было больше трех).
На рис. 6 изображено пространство толерантности
![](data:image/png;base64,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)
, состоящее из двух циклов, зацепленных в одной точке. Сопряженное пространство
![](data:image/png;base64,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)
состоит из таких же циклов с более сложным зацеплением. Но сопряженное к последнему пространство
![](data:image/png;base64,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)
по существу совпадает с исходным пространством
![](data:image/png;base64,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)
.
Определение. Пусть
![](data:image/png;base64,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)
– базис. Тогда пространство
![](data:image/png;base64,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)
называется
сопряженным к
![](data:image/png;base64,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)
,
относительно данного базиса ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAXCAYAAAD+4+QTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD2SURBVEjHY2hsbGSgNWYYtWRoWBJlzLCQgYHhPwzLuuUU4xMn2yc5brLFDAyybzzy6g2JESfLErCrjaMWEitOsiX19bGSxgwMd42jG3yIESfLkoZoYx8GBuO7sfX1ksSIUyXiUTCJQYXVko6ONB4PGYY96CmH3KDCakl9noehLIPsTfTUAwkq0lIVTkvASVTGY09aRwcPMeKIZI07/2BNVbiCClfmAwexrOxKkC9Bao0YjHYjJw6croFFMCFXwoNY1mMlyJfgYEXzMVXKJkh84U59VLEElORhqQ6ZTTVLwPEl5z4LFDyw5E9VS2AJglBmHa0ZScIAuB5EH3vCdoMAAAAASUVORK5CYII=)
.
Определение. Второе сопряженное пространство относительно некоторого базиса
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAXCAYAAAD+4+QTAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAD2SURBVEjHY2hsbGSgNWYYtWRoWBJlzLCQgYHhPwzLuuUU4xMn2yc5brLFDAyybzzy6g2JESfLErCrjaMWEitOsiX19bGSxgwMd42jG3yIESfLkoZoYx8GBuO7sfX1ksSIUyXiUTCJQYXVko6ONB4PGYY96CmH3KDCakl9noehLIPsTfTUAwkq0lIVTkvASVTGY09aRwcPMeKIZI07/2BNVbiCClfmAwexrOxKkC9Bao0YjHYjJw6croFFMCFXwoNY1mMlyJfgYEXzMVXKJkh84U59VLEElORhqQ6ZTTVLwPEl5z4LFDyw5E9VS2AJglBmHa0ZScIAuB5EH3vCdoMAAAAASUVORK5CYII=)
в
![](data:image/png;base64,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)
и базиса
![](data:image/png;base64,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)
в
![](data:image/png;base64,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)
называется
производным от исходного пространства толерантности
![](data:image/png;base64,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)
.
Итак, производное пространство толерантности определяется не однозначно, а с точностью до выбора базисов. Этот произвол исключается, когда
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
имеют по единственному базису.
Рассмотрим несколько примеров.
1. Для линейного графа с
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgFTMMIU319bGSxgwMdxkYGP7LuuUUE20TSKMRg+wpj7x6Q+I15XkYysp6rEzr6OAhWlOOm2wxg3HUQqL91NGRxuMhw7DHOLrBB2wjA8MbkP/Q/YjpNAajU7H19ZLgQDGOridoE8xpyJoJaooyZlgIcw4Dg/FdgpqQgxpik+xNXMEOZzREG/swyHjsAQU1LEBAngezPaKTsWoCOQ05hMD+AztT9g26jUMplROLAcI8Z5L9Aa5bAAAAAElFTkSuQmCC)
вершинами
![](data:image/png;base64,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)
производное пространство также есть линейный граф, но с
![](data:image/png;base64,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)
вершинами (см. рис. 4)
2. Для циклического графа с
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAATCAYAAABLN4eXAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC4SURBVDjLY2hsbGQgFTMMIU319bGSxgwMdxkYGP7LuuUUE20TSKMRg+wpj7x6Q+I15XkYysp6rEzr6OAhWlOOm2wxg3HUQqL91NGRxuMhw7DHOLrBB2wjA8MbkP/Q/YjpNAajU7H19ZLgQDGOridoE8xpyJoJaooyZlgIcw4Dg/FdgpqQgxpik+xNXMEOZzREG/swyHjsAQU1LEBAngezPaKTsWoCOQ05hMD+AztT9g26jUMplROLAcI8Z5L9Aa5bAAAAAElFTkSuQmCC)
вершинами
![](data:image/png;base64,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)
производное пространство "совпадает" с исходным пространством (см. рис. 5).
3. Та же ситуация для зацепленных циклических графов (см. рис. 6).
4. Для пространства
![](data:image/png;base64,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)
производное пространство
![](data:image/png;base64,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)
состоит из одного элемента.
2.6.5 Теорема
Если
– произвольное пространство толерантности, а
– произвольный базис в нем, то существует такой базис
в сопряженном пространстве
и такое инъективное отображение
, что при
и
из
следует
. Доказательство. Обозначим через
![](data:image/png;base64,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)
множество классов из базиса
![](data:image/png;base64,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)
, содержащих
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACYSURBVDjLY2hsbGQgFTMMIU0N0cY+DAwM/xkYZN945NUboojJeOxJ6+jgwWlTjptsMYNx1EIYTZTz6vM8DGUZGN7IuuUUE+2njo40Hg8Zhj3G0Q0+RGvKczNOMTGRXYHNaVg1gTwOchbYibIeK0GeBxkCCxgUTXkuslbAUGpgMI4OBPEnTpzI5iHPEAcSk3XJsxqqKYJYDAAk5hu1Oa8ZsQAAAABJRU5ErkJggg==)
. Для любых классов
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVEjHY2hsbGSgJmYYNZA2Bua4yRYzMDD8h2FZt5xiDHEZjz1pHR08RLuwIdrYB6TROLrBByZWn+dhKMtgdCq2vl6SZC+DXYPkiihjhoW4XEXQwI6ONB4PGYY9IK/W18dKGjMw3EV2KckGQrwme9PNzbiWgcH4Lj4vEmUgLPwYGGTfeOTVG1Icy+DwMvFYC/I2xS5EDjNYWBITGTgNhHgX4SqYBeiGwi1D8wHW2GUwjlqIGUkMb7AZ6i5nPAurgYiIQM0JGOJIOQevgeTgEWhgpDGDBjBMHRgkXfRDV61iHqElNgDecZyKNS3oQwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
из
![](data:image/png;base64,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)
имеем
![](data:image/png;base64,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)
, т.е.
![](data:image/png;base64,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)
. Итак, множества
![](data:image/png;base64,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)
суть предклассы в
![](data:image/png;base64,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)
. Значит, для всякого
![](data:image/png;base64,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)
существует класс в
![](data:image/png;base64,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)
, для которого
![](data:image/png;base64,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)
. Зафиксируем для каждого
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAC5SURBVDjLY2hsbGQgFTMMjCYgYARiJhDGIsaIVVNDrLE3UPIvA4Psa5esaiOQwvpIY1+wmKznrrSODh6czstxky1mMIpaBKaNoxcQ5af6PA9DWQaGN7JuOcVEB0R5eRqvhwzDHuPIel+iNIH8kedmnGJiIrucwThqIUwMqyZYKIE8LuuRVwR2oqzHytC0ND6QIR559YYYmvJcJIHeYHBgMI7UAPFXrQpldpFk0AeJSbrkyQ6CFEFTTQDxdAlpp7TWBAAAAABJRU5ErkJggg==)
некоторый класс
![](data:image/png;base64,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)
и множество этих классов обозначим через
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABASURBVDjLY2hsbGQgFzNQrLmjI43HQ4ZhD4Nx1EJsiqKMGRYyyHjsSevo4BnVjKyZgeE/TkwTmwcukYxqppNmAOJ4dH16GepLAAAAAElFTkSuQmCC)
. Мы имеем сюръекцию
![](data:image/png;base64,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)
, которое каждому
![](data:image/png;base64,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)
сопоставляет класс
![](data:image/png;base64,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)
. Покажем, что
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAABASURBVDjLY2hsbGQgFzNQrLmjI43HQ4ZhD4Nx1EJsiqKMGRYyyHjsSevo4BnVjKyZgeE/TkwTmwcukYxqppNmAOJ4dH16GepLAAAAAElFTkSuQmCC)
содержит некоторый базис
![](data:image/png;base64,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)
. Действительно, если
![](data:image/png;base64,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)
, то существует
![](data:image/png;base64,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)
, содержащийся в
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVEjHY2hsbGSgJmYYNZA2Bua4yRYzMDD8h2FZt5xiDHEZjz1pHR08RLuwIdrYB6TROLrBByZWn+dhKMtgdCq2vl6SZC+DXYPkiihjhoW4XEXQwI6ONB4PGYY9IK/W18dKGjMw3EV2KckGQrwme9PNzbiWgcH4Lj4vEmUgLPwYGGTfeOTVG1Icy+DwMvFYC/I2xS5EDjNYWBITGTgNhHgX4SqYBeiGwi1D8wHW2GUwjlqIGUkMb7AZ6i5nPAurgYiIQM0JGOJIOQevgeTgEWhgpDGDBjBMHRgkXfRDV61iHqElNgDecZyKNS3oQwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
. Тогда
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAXCAYAAAALHW+jAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAADmSURBVEjHY2hsbGSgJmYYNZA2Bua4yRYzMDD8h2FZt5xiDHEZjz1pHR08RLuwIdrYB6TROLrBByZWn+dhKMtgdCq2vl6SZC+DXYPkiihjhoW4XEXQwI6ONB4PGYY9IK/W18dKGjMw3EV2KckGQrwme9PNzbiWgcH4Lj4vEmUgLPwYGGTfeOTVG1Icy+DwMvFYC/I2xS5EDjNYWBITGTgNhHgX4SqYBeiGwi1D8wHW2GUwjlqIGUkMb7AZ6i5nPAurgYiIQM0JGOJIOQevgeTgEWhgpDGDBjBMHRgkXfRDV61iHqElNgDecZyKNS3oQwAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
содержаться в
![](data:image/png;base64,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)
, а значит,
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Теперь для каждого
![](data:image/png;base64,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)
выберем ровно один элемент
![](data:image/png;base64,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)
, для которого
![](data:image/png;base64,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)
. Множество таких элементов обозначим через
![](data:image/png;base64,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)
. Ясно, что
![](data:image/png;base64,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)
и возникающая при этом сюръекция
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAXCAYAAAARIY8tAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEwSURBVEjH7ZWxbcMwEEVvAA8QA6a6DOD8Hc4svIAtqBNcGUzh2qDUCcgG6ryHJ8gO3sA7ODhRdASaluUEAVKouEYk7/HeHSEqy5L+MmgE/E/AGnQgogsRTpm109ieIsXS7aGL4u3u6QpcAnXWxs7DNWv0XBGd+y7wEOCquAVU1WayQFILoO/mvQBrsykzv4PohLRYdtcMI2fGXtSEa4MBogdZlocAUQM2+ZbVboieu4AUsCtrXvWMjl6DqGHw3hTmRb4T1ocfTZHoAVJ77UObSNRIP3yDh+iJAho97WEP8Grk2zN6ogDR4w83ydTbJ6A/NlU1CavqTlajLQK+1ZMsap8sfAteT2w8m/FNUN8FuNLdy/Q36ar5ft1tRKroBfw2RsDDuPZopo9+SMY/2qD4AucgJWPF8wACAAAAAElFTkSuQmCC)
на
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABkAAAAYCAYAAAAPtVbGAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEaSURBVEjH7ZXNDYJAEIVfATZgwtiDuz3gHqxAw5UT4cLZrNxI7MAbR2vQCuyAAx3Yg2Yhi7iw8hO8GA6TmAnmm/fmDSCOY/y6MEP+GxK4FJEbRL0gO44UwFOX/qOtL6W35EDOuTi5Lj8A9BChXHcqUVOZD9v6CsLArozhCqKMwO6elMtOSDE136V9+4PtquTvj9s+/VGLP+75FuB5XfK3/iiIueCPslg1CJIk/kI4uJnejrWqFSJDsSZQZqaqtKqZtlGQIqKOuPlJsujTf8e6eT+tEG2Jzaq2eFYWE12USn0zrXdiTqMX3DVlZTGJi1JZ2GoonuSdVe7Lnr5JICryOnX135NBin2tNmdlj47/pBAdiK5jnb+Mg+oFBahlfPtOCH0AAAAASUVORK5CYII=)
инъективно. Тогда обратное к нему отображение
![](data:image/png;base64,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)
инъективно отображает
![](data:image/png;base64,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)
на подмножество
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABgAAAAXCAYAAAARIY8tAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAEwSURBVEjH7ZWxbcMwEEVvAA8QA6a6DOD8Hc4svIAtqBNcGUzh2qDUCcgG6ryHJ8gO3sA7ODhRdASaluUEAVKouEYk7/HeHSEqy5L+MmgE/E/AGnQgogsRTpm109ieIsXS7aGL4u3u6QpcAnXWxs7DNWv0XBGd+y7wEOCquAVU1WayQFILoO/mvQBrsykzv4PohLRYdtcMI2fGXtSEa4MBogdZlocAUQM2+ZbVboieu4AUsCtrXvWMjl6DqGHw3hTmRb4T1ocfTZHoAVJ77UObSNRIP3yDh+iJAho97WEP8Grk2zN6ogDR4w83ydTbJ6A/NlU1CavqTlajLQK+1ZMsap8sfAteT2w8m/FNUN8FuNLdy/Q36ar5ft1tRKroBfw2RsDDuPZopo9+SMY/2qD4AucgJWPF8wACAAAAAElFTkSuQmCC)
множества
![](data:image/png;base64,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)
. Поэтому его можно рассматривать как инъективное (но уже в общем случае не сюръективное) отображение. Пусть теперь
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADwAAAAZCAYAAABtnU33AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAMBSURBVFjD7VhBbtpAFP0DXSZqtqkYzlB76A1cxxGkXVktIC9rVQhZSkjkBWoHdixygi4iklVKL9A0zbpHqEpJ9lV7AxLSGYOR7YwNxm4VKV4MEt9jzX/z3/v/AXS7XXhI60GBzQBngGOswQBy7CN3H0BF5RL+AsCj+Zq97I/reXe/DpBvqriF1WZr9hyllbyuQ16US2h8QS7CQ5oa3kUA12zzLdt/jbXmLo9bGt5j3ycsPgasnZm93hqlxiYBNCLk+aGikvcA+LdmUSktwLUSHCEEN9NcYJ6LKL5MLqEH0SrZ4eCI0Sm7N9puaASD/M2gdHO+jx0ig/yZEPgCxeL34PM0FqvYPiCWfKvzNCq+TC7Rh2DtnFeR06RKcn23qmGscG8/tGGwG/TRMCCN0CrLcAKk3l82HpWL8ADbNte1AnzlOrAsoyADDIlBy0mqxLXBGVIE+OVIYr7kYRQjbNt4IgO6dJm2KL5Sl6aWJmHAQ0UhFIAM06CoI5EIhkRLS7qqWBb2MsN+Jb0EREZxcws/BKEJYqJXTLuUFGyvZ66pRKG6aW7EpXSNwDHL5cbPChgzbUxEdF4JsKON0vYnDcMZAnmkW3YhUXVn3TOY9CJKz6WlWXt36QyXpN6pJAbs1QavjAO6oF7opv04EeDi1gfTttfjvNduKDKT1o9gd57S/G7XjvIQoYDfVaUXXm1MqwNDSACaX9w2xqdx5dFQ8YE7KZaJezwE9wrcR4xZ490XAuZd1DT1DbUAFyC/PnG1xeO2qZRYx/gzBc106HU7up6/dcZNtBapQcoIyM9g8xG9x6tkWRUsAVxh9e0BP0MYF9hHRwYYf+TV52yVQD73SsaXkE9brpMKxvmtedxOjlT7tPpsZ9F4EZ4RomFeJd+eUu1IFBfNWmfC4K0BL0yb5xWYDIldUF3DFJP64X35NTRziA6dWTGOmfNc7KXj2T7yJk3vnNh7k9yxa0b4SAt28mS3yRoa18sq4+GfVNedBozCzoRhIy1VwNk/HhngDHAG+H+vv4fcRgjQZ1elAAAAAElFTkSuQmCC)
и,
![](data:image/png;base64,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)
где
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEUAAAAZCAYAAABnweOlAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAIPSURBVFjD7VhBbsIwENwH8AEk9tgHEPOGyKr4AETcKk4oF86V4Rap6iO4lUNfAC/IDzjwA/7QkrgbHMeOE4KqtPJhD8SOzY5nZteB7XYLPsrhQfCgeFA8KB6UlrEKcY3hav0nQBExHyPABQC+KFi0mZbmiMUwgOCwEGKoJqm+QwmXno/4MRazJwZwZoy/hSF7BcALj6Nnfb3egJIDgny/TJJBCSA239GcTcSmAOxsSkCOlUGUawQpzSdAgwAOgHiiMTkPTzwW436BYmBAm/GcFVc2EKhzBjv1t0s+OoD9kc818YzeJr1nSdp8IEmWAz6CYzZOa+iya+o1KjONoBAlpfYktYpn2inkJ6PouhKGzUyJAwZpgJCq60uWYGqjN9Ff+oRZXs09rcqWWgRtSHYNApROV2dMnZfYDq8LU3WW1VaFNmWsC2VJDvRcVhE7KDmoE/6Zv9OFKRb5Qp1m63R6j3xsrq+fWB0o6twCTIvBPhSUOGQvkwl+PFo6tmT1SuIuxbcxSuweYBrLJ9s0d3Wlj8hA6qJd3QvUk9EBqTNaXWaVJrAlME6jLbrBnw2LP6Al8SiT1btRV0m+meutY80AqDxX1sz3uuZjY16jktyncJXlphFxFMjm722aw15f5FzteJMwSd/V8PX+hutq913vcsR96X7UYL1/+7mATHQmZmPbVcJ/ZPIfmTwoHpTfiG+IId88IoWQvQAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
. Тогда существует класс
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAARCAYAAAA7bUf6AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACZSURBVDjLY2hsbGSgFDMMbkNy3GSLGRgY/sOwrFtOMYa4jMeetI4OHrwuaYg29gEpNo5u8IGJ1ed5GMoyGJ2Kra+XJMo7YFuRbIsyZliIzCdoSEdHGo+HDMMekDfq62MljRkY7iK7iChDIM6WvenmZlzLwGB8F935RBkCCw8GBtk3Hnn1hmTFDtj/Jh5rQV4i2yXDLMWOcEMAA6ao8LGrlm8AAAAASUVORK5CYII=)
, содержащий
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA0AAAAPCAYAAAA/I0V3AAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACYSURBVDjLY2hsbGQgFTMMIU0N0cY+DAwM/xkYZN945NUboojJeOxJ6+jgwWlTjptsMYNx1EIYTZTz6vM8DGUZGN7IuuUUE+2njo40Hg8Zhj3G0Q0+RGvKczNOMTGRXYHNaVg1gTwOchbYibIeK0GeBxkCCxgUTXkukkBvMDgwGEdqgPirVoUyu0gy6IPEJF3yZIdqiiAWAwAGvxqCwfJaXAAAAABJRU5ErkJggg==)
и
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAA8AAAARCAYAAAACCvahAAAAAXNSR0ICQMB9xQAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAACQSURBVDjLY2hsbGQgFzMMHs1RxgwLGRgY/jPIeOxJ6+jgAYk1RBv7IPPx2gxWzGB8N7a+XhLE7+hI43EzdqslSnN9noehLIPsTY+8ekMwvz5W0s0tL4woP4MUGzMw3DWObvAB8fPc3MJgriBJM8gVxm55KUSHNsiPHjIMe2Q9PXuM5dxnoft1EMbzqGYaagYA36t6+BYlJoYAAAAASUVORK5CYII=)
. Значит,
![](data:image/png;base64,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)
. Но из
![](data:image/png;base64,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)
и
![](data:image/png;base64,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)
следует, что
![](data:image/png;base64,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)
, т.е.
![](data:image/png;base64,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)
. Теорема доказана.