An answer to a question of Coleman on scattered sets

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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.
5 pages

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General Topology, 54G12; 54H05; 68U05; 68U10

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http://salesiana.dossiersoluciones.com/handle/123456789/77545

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9810077
 http://arxiv.org/abs/math/9810077

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arXiv