An answer to a question of Coleman on scattered sets

The aim of this paper is to show that every scattered subset of a dense-in-itself semi-\(T_D\)-space is nowhere dense. We are thus able to answer a recent question of Coleman in the affirmative. In terms of Digital Topology, we prove that in semi-\(T_D\)-spaces with no open screen, trace spaces have...

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Bibliographic Details
Published in:arXiv.org 1998-10
Main Authors: Dontchev, Julian, Ganster, Maximilian
Format: Article
Language:English
Subjects:
Topology
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Summary:The aim of this paper is to show that every scattered subset of a dense-in-itself semi-\(T_D\)-space is nowhere dense. We are thus able to answer a recent question of Coleman in the affirmative. In terms of Digital Topology, we prove that in semi-\(T_D\)-spaces with no open screen, trace spaces have no consolidations.
ISSN:2331-8422