Browder’s theorem with general parameter space

Eilon Solan, Omri N. Solan

Research output: Contribution to journalArticlepeer-review

Abstract

It follows from Browder (Summa Bras Math 4:183–191, 1960) 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 a locally convex linear vector space, the set of fixed points of F, defined by CF: = { (x, y) ∈ X× Y: F(x, y) = y} , has a connected component whose projection to the first coordinate is X. We extend Browder’s result to the case that X is a connected and compact Hausdorff space.

Original languageEnglish
Article number10
JournalJournal of Fixed Point Theory and Applications
Volume24
Issue number1
DOIs
StatePublished - Feb 2022

Keywords

  • Browder’s theorem
  • connected component
  • fixed points
  • index theory

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