Pointwise-recurrent maps on uniquely arcwise connected locally arcwise connected spaces

We prove that self-mappings of uniquely arcwise connected locally arcwise connected spaces are pointwise-recurrent if and only if all their cutpoints are periodic while all endpoints are either periodic or belong to what we call "topological weak adding machines". We also introduce the not...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2015-03
Main Author: Blokh, Alexander M
Format: Article
Language:English
Subjects:
Topology
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that self-mappings of uniquely arcwise connected locally arcwise connected spaces are pointwise-recurrent if and only if all their cutpoints are periodic while all endpoints are either periodic or belong to what we call "topological weak adding machines". We also introduce the notion of a \emph{ray complete} uniquely arcwise connected locally arcwise connected space and show that for them the above "topological weak adding machines" coincide with classical adding machines (e.g., this holds if the entire space is compact).
ISSN:2331-8422