An Essay on Perfection

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1987 English Publisher:Maynooth UniversityJournal:Irish Mathematical Society Bulletin, volume 18, pages 9-17 (issn: 0791-5578,

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Authors: Ó'Searcóid, Mícheál;

doi: 10.33232/bims.0018.9.17

An Essay on Perfection

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Abstract

The author introduces a generalization by means of the concepts of compactness and G-sets. Using some properties introduced of these new concepts, some general results are given about topological spaces which must contain perfect sets. To show the absence of perfect sets without some of these properties several counter-examples are given.

Keywords

transfinite cardinal numbers, Counterexamples in general topology, separability, perfect sets, Fairly general properties of topological spaces, \(\Omega \)-compact space, metrizability, G-sets

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