ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS

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Rostami Salimeh; Ahmadi Zand Mohammadreza

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Journal: JOURNAL OF ALGEBRAIC SYSTEMS Year:2020 | Volume:8 | Issue:1 Page(s): 17-26

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Information Journal Paper

Title

ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS

Author(s)

Rostami Salimeh | Ahmadi Zand Mohammadreza | Issue Writer Certificate

Keywords

ω-narrow topological generalized group

Resolvable topological generalizad group

Precompact topological generalized group

Invariance number

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.

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APA: Copy

Ahmadi Zand, Mohammadreza, & Rostami, Salimeh. (2020). ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS. JOURNAL OF ALGEBRAIC SYSTEMS, 8(1 ), 17-26. SID. https://sid.ir/paper/378456/en

Vancouver: Copy

Ahmadi Zand Mohammadreza, Rostami Salimeh. ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS. JOURNAL OF ALGEBRAIC SYSTEMS[Internet]. 2020;8(1 ):17-26. Available from: https://sid.ir/paper/378456/en

IEEE: Copy

Mohammadreza Ahmadi Zand, and Salimeh Rostami, “ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS,” JOURNAL OF ALGEBRAIC SYSTEMS, vol. 8, no. 1 , pp. 17–26, 2020, [Online]. Available: https://sid.ir/paper/378456/en

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