The dimension of hyperspaces of non-metrizable continua

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2012Embargo end date: 01 Sep 2012 English Publisher:Institute of Mathematics, Polish Academy of SciencesJournal:Colloquium Mathematicum, volume 128, pages 101-107 (issn: 0010-1354, eissn: 1730-6302,

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Authors: Stadnicki, Wojciech;

doi: 10.4064/cm128-1-9 , 10.48550/arxiv.1209.3443

arXiv: 1209.3443

The dimension of hyperspaces of non-metrizable continua

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Abstract

We prove that, for any Hausdorff continuum X, if dim X > 1 then the hyperspace C(X) of subcontinua of X is not a C-space; if dim X = 1 and X is hereditarily indecomposable then dim C(X) = 2 or C(X) is not a C-space. This generalizes results known for metric continua.

6 pages, to be published in Colloquium Mathematicum

Related Organizations

University of Wrocław
Poland

Keywords

General Topology (math.GN), FOS: Mathematics, Mathematics - Logic, Logic (math.LO), 54F45 (Primary) 03C98, 54B20 (Secondary), Mathematics - General Topology

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