Lattice-Invariant Topological Properties

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Aug 1972Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 34, page 565 (issn: 0002-9939,

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Authors: Sharma, P. L.;

doi: 10.2307/2038407 , 10.1090/s0002-9939-1972-0295277-2

Lattice-Invariant Topological Properties

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Abstract

The purpose of this paper is to show that an isomorphism between the lattices of all closed sets of two topological spaces induces an isomorphism on the lattices of their zero-sets. This is achieved by showing that any continuous real-valued function on a space X can be transferred to any space lattice-equivalent to X. Several topological properties are shown to be lattice-invariant.

Keywords

Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.), Noncompact covering properties (paracompact, Lindelöf, etc.), Continuous maps

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