The Implicit Function Theorem for continuous functions

2007/06/26 by Carlos Biasi, Biasi, Carlos, Carlos Gutierrez +3 · 2 citations
Mathematics · #58C15: 47J07 #Algebraic Topology (math.AT) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AT #math.CA #msc:47J07

paper · pdf · doi:10.48550/arxiv.0706.3905

9 pages, no figures

arxiv created 2007/06/26 · arxiv updated 2009/12/01

Abstract

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of these classic theorems are proved when we consider differenciable (not necessarily C¹) maps.

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• On the Piecewise Linear Perturbations of the Doubling Map
• The Aubin Property for Generalized Equations over C²-cone Reducible Sets

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