2007/12/17 by Toshizumi Fukui, Krzysztof Kurdyka, Fukui, Toshizumi +3
Mathematics · #03C64 (Primary) #14P10 #32F27 #52Axx #58A35 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:03C64 #msc:14P10 #msc:32F27 #msc:52Axx #msc:58A35
paper · pdf · doi:10.48550/arxiv.0712.2476
19 pages
arxiv created 2007/12/17 · arxiv updated 2009/12/01
We give several versions of local and global inverse mapping theorem for tame non necessarily smooth, mappings. Here tame mapping means a mapping which is subanalytic or, more generally, definable in some o-minimal structure. Our sufficient conditions are formulated in terms of various properties (convexity, positivity of some principal minors, contractiblity) of the space of Jacobi's matrices at smooth points.