Global -neighborhood groups

Bayoumi, Fatma

doi:10.1016/j.fss.2007.10.006

Cited by 6 publications

(1 citation statement)

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“…3 Since then quite a good number of research articles have appeared on a fuzzy topological group. [4][5][6][7][8][9][10][11][12][13][14] It is a well established fact that the topology of a topological group is determined by the identity element of the group which permits the localization of many notions in classical topological groups 15 ; but neither Foster nor Katsaras considered this fact in their ½0; 1-valued generalizations 1,3 of classical notions. Later on, of course, with the help of the Lowen-fuzzy neighborhood system, 16 Katsaras introduced the notion of a linear fuzzy neighborhood space, which obviously yields localizable structure.…”

Section: Introductionmentioning

confidence: 99%

Enriched Lattice-Valued Topological Groups

Ahsanullah

Gauld

Al-Mufarrij

et al. 2014

New Math. and Nat. Computation

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In this paper, we focus on enriched cl-premonoid-valued topological groups, and their so-called change-of-basis lattice. In so doing, we take L as an enriched cl-premonoid and present a category SL-NTopGrp, of strati¯ed enriched cl-premonoid-valued neighborhood topological groups. We produce some characterization theorems, and prove that every strati¯ed L-neighborhood topological group is uniformizable. Finally, we look at the enriched lattice-valued neighborhood topological group when the underlying basis is changed under certain functorial mechanism.

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