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Search: MSC category 52B99 ( None of the above, but in this section )

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1. CJM 2010 (vol 62 pp. 975)

Bjorndahl, Christina; Karshon, Yael
 Revisiting Tietze-Nakajima: Local and Global Convexity for Maps A theorem of Tietze and Nakajima, from 1928, asserts that if a subset $X$ of $\mathbb{R}^n$ is closed, connected, and locally convex, then it is convex. We give an analogous local to global convexity" theorem when the inclusion map of $X$ to $\mathbb{R}^n$ is replaced by a map from a topological space $X$ to $\mathbb{R}^n$ that satisfies certain local properties. Our motivation comes from the Condevaux--Dazord--Molino proof of the Atiyah--Guillemin--Sternberg convexity theorem in symplectic geometry. Categories:53D20, 52B99

2. CJM 2004 (vol 56 pp. 472)