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In mathematics, Ky Fan's lemma (KFL) is a combinatorial lemma about labellings of triangulations. It is a generalization of Tucker's lemma. It was proved by Ky Fan in 1952. == Definitions == KFL uses the following concepts. * : the closed ''n''-dimensional ball. * * : its boundary sphere. * ''T'': a triangulation of . * * ''T'' is called ''boundary antipodally symmetric'' if the subset of simplices of ''T'' which are in provides a triangulation of where if σ is a simplex then so is −σ. * ''L'': a ''labeling'' of the vertices of ''T'', which assigns to each vertex a non-zero integer: . * * ''L'' is called ''boundary odd'' if for every vertex , . * An edge of ''T'' is called a ''complementary edge'' of ''L'' if the labels of its two endpoints have the same size and opposite signs, e.g. . * An ''n''-dimensional simplex of ''T'' is called an ''alternating simplex'' of ''L'' if its labels have different sizes with alternating signs, e.g. or . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ky Fan lemma」の詳細全文を読む スポンサード リンク
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