An answer to a question of Coleman on scattered sets

Details An answer to a question of Coleman on scattered sets An answer to a question of Coleman on scattered sets

1998-10-12

arxiv.org/abs/math/9810077v1

Mathematics

General Topology

5 pages

Scientific paper

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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