Inverse mapping theorem and local forms of continuous mappings

Autor(es)

Barreto, A. P. ^[1] ; Fenille, M. C. ^[2] ; Hartmann, L. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil

^[2] Univ Fed Uberlandia, Fac Matemat, BR-38408100 Uberlandia, MG - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Topology and its Applications; v. 197, p. 10-20, JAN 1 2016.
• Citações Web of Science: 0

Resumo

We present a homological version of the Inverse Mapping Theorem for open and discrete continuous maps between oriented topological manifolds, with assumptions on the degree of the maps, but without any assumption on differentiability. We prove that this theorem is equivalent to the known homological version of the Implicit Mapping Theorem. Additionally, we study conditions for a map between oriented topological manifolds to be locally like an injection or a projection, via alternative notions of topological immersions and submersions. (C) 2015 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 12/24454-8 - Topologia algébrica, geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático