Browder's Theorem with General Parameter Space

2021/04/29 by Solan, Eilon, Solan, Omri Nisan
#55M20 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2104.14612

Abstract

Browder (1960) proved that for every continuous function F : X × Y → Y, where X is the unit interval and Y is a nonempty, convex, and compact subset of \dRⁿ, the set of fixed points of F, defined by C_F := \ (x,y) ∈ X × Y \colon F(x,y)=y\ has a connected component whose projection to the first coordinate is X. We extend this result to the case where X is a connected and compact Hausdorff space.

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