TY - JOUR
ID - 1763
TI - ω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Ahmadi Zand, M. R.
AU - Rostami, S.
AD - Department of Mathematics, Yazd University, P.O. Box 89195 - 741, Yazd, Iran.
Y1 - 2020
PY - 2020
VL - 8
IS - 1
SP - 17
EP - 26
KW - ω-narrow topological generalized group
KW - Resolvable topological generalizad group
KW - Precompact topological generalized group
KW - Invariance number
DO - 10.22044/jas.2019.8356.1409
N2 - Abstract. A topological group H is called ω -narrow if for everyneighbourhood V of it’s identity element there exists a countableset 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) ∈ Gsuch that xe(x) = e(x)x = x and for every x ∈ G there existsx − 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} iscountable and for any a ∈ G, {x ∈ G|e(x) = e(a)} is an ω-narrowtopological group, then G is called an ω-narrow topological generalized group. In this paper, ω-narrow and resolvable topologicalgeneralized groups are introduced and studied
UR - https://jas.shahroodut.ac.ir/article_1763.html
L1 - https://jas.shahroodut.ac.ir/article_1763_7eca9f8c7119e52f92adbafaae64e02c.pdf
ER -