Cleavability over reals
type: Item
instance of: scholarly article
title: Cleavability over reals
zbMATH Open document ID: 0786.54015
DOI: 10.1016/0166-8641(92)90024-T
published in: Topology and its Applications
publication date: 1993-05-16T00:00:00Z
review text: A space \(X\) is cleavable over reals \(\mathbb{R}\) if for every subset \(A\) of \(X\) there exists a continuous mapping \(f: X\to\mathbb{R}\) such that \(f^{-1} f(A)= A\). The paper studies the structure of spaces which are cleavable over \(\mathbb{R}\). The main result: Every compactum which is cleavable over \(\mathbb{R}\) is homeomorphic to a subspace of \(\mathbb{R}\); in particular, if a nontrivial continuum is cleavable over \(\mathbb{R}\), then it is homeomorphic to the unit segment \([0,1]\).
Mathematics Subject Classification ID: 54C10
Mathematics Subject Classification ID: 54F15
Mathematics Subject Classification ID: 54F50
Mathematics Subject Classification ID: 54F55
Mathematics Subject Classification ID: 54F65
zbMATH DE Number: 166417
zbMATH Keywords: cleavability over \(\mathbb{R}\),
zbMATH Keywords: \(c\)-simple space
zbMATH Keywords: \(c\)-thick space
zbMATH Keywords: continuum
zbMATH Keywords: dendrite
zbMATH Keywords: unicoherence
author: A. V. Arhangel'skii
reviewed by: Ljubiša D. R. Kočinac
MaRDI profile type: Publication
cites work: A dichotomy theorem and other results for a class of quotients of topological groups
cites work: Q3029790
cites work: Q3814168
cites work: Q4150803
cites work: Q4482418
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full work available at URL: 0166-8641(92)90024-t
OpenAlex ID: W2116186964
description: scientific article; zbMATH DE number 166417