Some properties of cleavable spaces
type: Item
instance of: scholarly article
title: Some properties of cleavable spaces
zbMATH Open document ID: 0820.54002
DOI: 10.1016/0166-8641(95)92520-R
author: Andrew N. Yakivchik
published in: Topology and its Applications
publication date: 1995-09-17T00:00:00Z
review text: A space \(X\) is said to be cleavable over a class \({\mathcal P}\) of topological spaces if for every subset \(A\) of \(X\) there are \(Y\in {\mathcal P}\) and a continuous mapping \(f: X\to Y\) such that \(f^{-1} f(A)=A\). The author proves that cleavability over the class of all spaces having weight \(\leq\tau\) and over the class of all metrizable spaces (with weight \(\leq\tau\)) is an invariant of open perfect mappings. If an arcwise connected space is cleavable over the class \({\mathcal P}\) of all spaces of countable weight, then it admits a continuous bijection onto a space in \({\mathcal P}\). Two examples are given.
Mathematics Subject Classification ID: 54A25
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54C99
Mathematics Subject Classification ID: 54D05
zbMATH DE Number: 735674
zbMATH Keywords: cleft cardinal function
zbMATH Keywords: open perfect mapping
zbMATH Keywords: cleavability
zbMATH Keywords: arcwise connected space
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
cites work: Q3049484
cites work: Q3029790
cites work: Q3831671
cites work: Q3684795
cites work: Q3814168
cites work: Q4150804
cites work: Q3270120
cites work: On the diagonal number of topological spaces
description: scientific article; zbMATH DE number 735674