A Topological Coincidence Theory for Multifunctions via Homotopy

Donal O’Regan

doi:10.3390/math8030427

Abstract

A new simple result is presented which immediately yields the topological transversality theorem for coincidences.

Highlights

The topological transversality theorem of Granas [1] states that if F and G are continuous compact single valued maps and F ∼
In this paper we approach this differently and we present a very general topological transversality theorem for coincidences
For convenience we desribe a class of maps one could consider in this setting

Summary

Introduction

The topological transversality theorem of Granas [1] states that if F and G are continuous compact single valued maps and F ∼= G F is essential if and only if G is essential. Is Tychonoff and not normal the one can replace the compactness of the map in A(U, E), Definition 3 and Remark 2 with any condition that guarantees that K in the proof of Theorem 1 is compact.

Results

Conclusion