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Revisiting Tietze-Nakajima: Local and Global Convexity for Maps

2010
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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A theorem of Tietze and Nakajima, from 1928, asserts that if a subset X of R n is closed, connected, and locally convex, then it is convex [Ti, N]. There are many generalizations of this "local to global convexity" phenomenon in the literature; a partial list is [BF, C, Ka, KW, Kl, SSV, S, Ta]. This paper contains an analogous "local to global convexity" theorem when the inclusion map of X to R n is replaced by a map from a topological space X to R n that satisfies certain local properties: We

doi:10.4153/cjm-2010-052-5
fatcat:srs3cc24wzcm3bomu4lc57acj4