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\(T\)-locality groups. (English) Zbl 1302.57070

Summary: The aim of this paper is to introduce the concepts of \(T\)-locality groups, where \(T\) stands for any continuous triangular norm. Our construct mainly will deal and relate with both fuzzy \(T\)-locality spaces and fuzzy \(TL\)-uniform spaces. We establish some basic results and characterization theorems of \(T\)-locality groups. We give the necessary and sufficient conditions for a group structure and a fuzzy \(T\)-locality system to be compatible. Moreover, we show that all initial and final lifts exist uniquely in the concrete category of \(T\)-locality groups and hence all initial and final \(T\)-locality groups exist and can be characterized. As consequences the \(T\)-locality subgroups, \(T\)-locality product groups and \(T\)-locality quotient groups exist.

MSC:

57T20 Homotopy groups of topological groups and homogeneous spaces
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