An answer to a question of Coleman on scattered sets
Julian Dontchev, Maximilian Ganster
Abstract
The aim of this paper is to show that every scattered subset of a dense-in-itself semi-TD-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-TD-spaces with no open screen, trace spaces have no consolidations.
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