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

Topological Algebra and its Applications (2013)

- Volume: 1, page 1-8
- ISSN: 2299-3231

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topTaras Banakh, and Igor Guran. "Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology." Topological Algebra and its Applications 1 (2013): 1-8. <http://eudml.org/doc/266852>.

@article{TarasBanakh2013,

abstract = {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.},

author = {Taras Banakh, Igor Guran},

journal = {Topological Algebra and its Applications},

keywords = {Semi-Zariski topology; supt-perfect semigroup; σ-discrete space; the group of finitely supported permutations; the semigroup of finitely supported relations; semi-Zariski topology; -discrete space; group of finitely supported permutations; semigroup of finitely supported relations},

language = {eng},

pages = {1-8},

title = {Perfectly supportable semigroups are σ-discrete in each Hausdorff shift-invariant topology},

url = {http://eudml.org/doc/266852},

volume = {1},

year = {2013},

}

TY - JOUR

AU - Taras Banakh

AU - Igor Guran

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

JO - Topological Algebra and its Applications

PY - 2013

VL - 1

SP - 1

EP - 8

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/266852

ER -

## References

top- [1] T. Banakh, The Solecki submeasures on groups, preprint (http://arxiv.org/abs/1211.0717).
- [2] T. Banakh, I. Guran, I. Protasov, Algebraically determined topologies on permutation groups, Topology Appl. 159:9 (2012) 2258–2268.[WoS] Zbl1277.20006
- [3] T. Banakh, I. Protasov, O. Sipacheva, Topologization of sets endowed with an action of a monoid, preprint (http://arxiv.org/abs/1112.5729). Zbl1294.54020
- [4] E. Gaughan, Group structures of infinite symmetric groups, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 907–910. Zbl0153.04301
- [5] I. Guran, O. Gutik, O. Ravsky, I. Chuchman, On symmetric topologiacl semigroups and groups, Visnyk Lviv Univ. Ser. Mech. Math. 74 (2011), 61–73 (in Ukrainian). Zbl1249.22002
- [6] D.Mauldin (ed.), The Scottish Book. Mathematics from the Scottish Café, Birkhauser, Boston, Mass., 1981. Zbl0485.01013
- [7] S. Ulam, A Collection of Mathematical Problems, Intersci. Publ., NY, 1960.

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