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An answer to a question of Coleman on scattered sets

Julian Dontchev·Maximilian Ganster
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Abstract

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.

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Julian Dontchev, Maximilian Ganster. 1998-10-12. An answer to a question of Coleman on scattered sets. https://arxiv.org/abs/math/9810077

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