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Topological Algebra and its Applications

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Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology

Taras Banakh / Igor Guran
Published Online: 2013-05-06 | DOI: https://doi.org/10.2478/taa-2013-0001


In this paper we introduce perfectly supportable semigroups and prove that they are σ-discrete in each Hausdorff shiftinvariant topology. The class of perfectly supportable semigroups includes each semigroup S such that FSym(X) ⊂ S ⊂ FRel(X) where FRel(X) is the semigroup of finitely supported relations on an infinite set X and FSym(X) is the group of finitely supported permutations of X.

Keywords: Semi-Zariski topology; supt-perfect semigroup; σ-discrete space; the group of finitely supported permutations; the semigroup of finitely supported relations

MSC: 20M20; 20B35; 22A15; 22A05; 54D45

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About the article

Received: 2012-07-31

Accepted: 2012-11-25

Published Online: 2013-05-06

Citation Information: Topological Algebra and its Applications, Volume 1, Pages 1–8, ISSN (Online) 2299-3231, DOI: https://doi.org/10.2478/taa-2013-0001.

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©2013 Versita Sp. z o.o.. This content is open access.

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