Revisiting tietze-nakajima: Local and global convexity for maps

Christina Bjorndahl*, Yael Karshon

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


A theorem of Tietze and Nakajima, from 1928, asserts that if a subset X of ℝn 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 ℝn is replaced by a map from a topological space X to ℝn that satisfies certain local properties. Our motivation comes from the Condevaux-Dazord-Molino proof of the Atiyah-Guillemin-Sternberg convexity theorem in symplectic geometry.

Original languageEnglish
Pages (from-to)975-993
Number of pages19
JournalCanadian Journal of Mathematics
Issue number5
StatePublished - Oct 2010
Externally publishedYes


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