ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS | ||
| Journal of Algebraic Systems | ||
| مقاله 3، دوره 8، شماره 1، آذر 2020، صفحه 17-26 اصل مقاله (145.29 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.8356.1409 | ||
| نویسندگان | ||
| M. R. Ahmadi Zand* ؛ S. Rostami | ||
| Department of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran. | ||
| چکیده | ||
| Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also let G be a topological space and the operation and inversion mapping are continuous, then G is called a topological generalized group. If {e(x) | x ∈ G} is countable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrow topological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topological generalized groups are introduced and studied | ||
| کلیدواژهها | ||
| ω-narrow topological generalized group؛ Resolvable topological generalizad group؛ Precompact topological generalized group؛ Invariance number | ||
| مراجع | ||
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