Cleavability over scattered first-countable LOTS
type: Item
instance of: scholarly article
title: Cleavability over scattered first-countable LOTS
zbMATH Open document ID: 1252.54009
author: Shari Levine
published in: Topology and its Applications
publication date: 2012-09-19T00:00:00Z
reviewed by: Jorge Picado
Mathematics Subject Classification ID: 54C05
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 03E10
zbMATH DE Number: 6084117
zbMATH Keywords: cleavability
zbMATH Keywords: linearly ordered topological space (LOTS)
zbMATH Keywords: first-countable
zbMATH Keywords: scattered
zbMATH Keywords: homeomorphism
MaRDI profile type: Publication
full work available at URL: j.topol.2012.07.005
OpenAlex ID: W2074938345
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DOI: 10.1016/J.TOPOL.2012.07.005
review text: A space \(X\) is \textit{cleavable} over a space \(Y\) \textit{along} \(A\subseteq X\) if there exists a continuous \(f: X\to Y\) such that \(f(A)\cap f(X\smallsetminus A)=\emptyset\). A space \(X\) is \textit{cleavable over} \(Y\) if it is cleavable over \(Y\) along all \(A\subseteq X\).NEWLINENEWLINEIn the present paper, the author examines cleavability over scattered first-countable LOTS, specifically cleavability over \(\omega_1\), answering some questions of \textit{A. V. Arhangel'skiĭ} [Ann. N. Y. Acad. Sci. 659, 18--28 (1992; Zbl 1250.54004)]. The main result asserts that if \(X\) is an infinite compactum cleavable over an infinite first-countable scattered LOTS, then \(X\) must be homeomorphic to a countable ordinal, and must also therefore be a LOTS.
description: scientific article; zbMATH DE number 6084117