Shadowing for induced maps of hyperspaces

Research output: Contribution to journalArticle

Authors

Colleges, School and Institutes

External organisations

  • School of Mathematics, Watson Building; University of Birmingham; Edgbaston Birmingham B15 2TT UK

Abstract

Given a nonempty compact metric space X and a continuous
function f : X → X, we study shadowing and h-shadowing for
the induced maps on hyperspaces, particularly in symmetric products,
Fn(X), and the hyperspace of compact subsets of X, 2X. We prove
that f has shadowing (h-shadowing) if and only if 2f has shadowing
(h-shadowing).

Details

Original languageEnglish
Pages (from-to)277-286
Number of pages10
JournalFundamenta Mathematicae
Volume235
Early online date4 Jul 2016
Publication statusPublished - 2016

Keywords

  • shadowing, pseudo orbit tracing, induced map, hyperspace