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

• Autorzy: Taras Banakh , Igor Guran
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.
• 22A15: Structure of topological semigroups
• 22A05: Structure of general topological groups
• 20B35: Subgroups of symmetric groups
• 54D45: Local compactness, σ -compactness

• Wydawca: De Gruyter Open
• Czasopismo: Topological Algebra and its Applications
• Rocznik: 2013
• Tom: 1
• Strony: 1-8

Daty

otrzymano

2012-07-31

zaakceptowano

2012-11-25

online

2013-05-06

Twórcy

autor

Taras Banakh

• Jan Kochanowski University in Kielce, Poland
• Ivan Franko National University of Lviv, Ukraine

autor

Igor Guran

• Ivan Franko National University of Lviv, Ukraine

Bibliografia

• [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]
• [3] T. Banakh, I. Protasov, O. Sipacheva, Topologization of sets endowed with an action of a monoid, preprint (http://arxiv.org/abs/1112.5729).
• [4] E. Gaughan, Group structures of infinite symmetric groups, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 907–910.
• [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).
• [6] D.Mauldin (ed.), The Scottish Book. Mathematics from the Scottish Café, Birkhauser, Boston, Mass., 1981.
• [7] S. Ulam, A Collection of Mathematical Problems, Intersci. Publ., NY, 1960.

Identyfikatory

DOI

10.2478/taa-2013-0001