A characterization of spaces that are the continuous image of an arc
type: Item
instance of: scholarly article
title: A characterization of spaces that are the continuous image of an arc
zbMATH Open document ID: 0604.54030
DOI: 10.1016/0166-8641(86)90066-0
author: L. B. Treybig
published in: Topology and its Applications
publication date: 1986-01-01T00:00:00Z
review text: \textit{S. Mardešić} and \textit{P. Papić} [Mat. Biblioteka, Beograd 25, 11-23 (1963)] defined two classes G and K of Hausdorff spaces that are the continuous images of an arc and of an ordered compactum, respectively. Answering some of their questions the author proves the following Theorem 3. A Hausdorff space M is in G if and only if M is a locally connected continuum such that M is in K. Another interesting result, Theorem 2, is related to some results obtained by \textit{W. Bula} and \textit{M. Turzański} [same journal 22, 7-17 (1986; Zbl 0587.54053)]. \{Reviewer's remark: For further results in this area see \textit{J. Nikiel}, ''Images of arcs - a nonseparable version of the Hahn- Mazurkiewicz theorem'', Fundam. Math. (to appear).\}
Mathematics Subject Classification ID: 54F05
Mathematics Subject Classification ID: 54F15
zbMATH DE Number: 3975857
zbMATH Keywords: compact ordered space
zbMATH Keywords: local connectivity
zbMATH Keywords: upper semi-continuous decomposition
zbMATH Keywords: Hahn-Mazurkiewicz theorem
zbMATH Keywords: continuous images
zbMATH Keywords: arc
reviewed by: Janusz J. Charatonik
MaRDI profile type: Publication
full work available at URL: 0166-8641(86)90066-0
OpenAlex ID: W1983260599
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description: scientific article; zbMATH DE number 3975857