Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces.
type: Item
instance of: scholarly article
title: Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces.
zbMATH Open document ID: 1041.54034
DOI: 10.1016/S0166-8641(03)00039-7
author: Guram Bezhanishvili
author: Ray Mines
author: Patrick Morandi
published in: Topology and its Applications
publication date: 2003-09-04T00:00:00Z
review text: In the present interesting paper the authors show that a space is Hausdorff-reducible if and only if it is hereditarily irresolvable, and offer several equivalent characterizations of hereditarily irresolvable and scattered spaces. They also show that for filtral topologies each of the three notions of submaximal, hereditarily irresolvable and Hausdorff-reducible coincide with the fact that the nonempty open sets form an ultrafilter. The authors construct by expanding some examples by El'kin, Padmavally and Anderson a compact irreducible \(T_1\)-space and a connected Hausdorff space, each of which is strongly irresolvable. Finally, the authors prove that the three notions of scattered, Hausdorff-reducible and hereditarily irresolvable coincide for a large class of spaces, including metric, Alexandroff, first countable, locally compact Hausdorff and spectral spaces.
Mathematics Subject Classification ID: 54G12
zbMATH DE Number: 1974780
zbMATH Keywords: Scattered space
zbMATH Keywords: Hausdorff-reducible space
zbMATH Keywords: Hereditarily irresolvable space
zbMATH Keywords: Strongly irresolvable space
reviewed by: Chariklia Konstadilaki
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1974780