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.
@article{bwmeta1.element.doi-10_2478_taa-2013-0001,
author = {Taras Banakh and Igor Guran},
title = {Perfectly supportable semigroups are $\sigma$-discrete in each Hausdorff shift-invariant topology},
journal = {Topological Algebra and its Applications},
volume = {1},
year = {2013},
pages = {1-8},
zbl = {1279.22003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0001}
}
Taras Banakh; Igor Guran. Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology. Topological Algebra and its Applications, Tome 1 (2013) pp. 1-8. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_taa-2013-0001/
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