TY - JOUR
T1 - Revisiting tietze-nakajima
T2 - Local and global convexity for maps
AU - Bjorndahl, Christina
AU - Karshon, Yael
PY - 2010/10
Y1 - 2010/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80053270375&partnerID=8YFLogxK
U2 - 10.4153/CJM-2010-052-5
DO - 10.4153/CJM-2010-052-5
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AN - SCOPUS:80053270375
SN - 0008-414X
VL - 62
SP - 975
EP - 993
JO - Canadian Journal of Mathematics
JF - Canadian Journal of Mathematics
IS - 5
ER -