K. Fan’s theorem in fuzzifying topology. (English) Zbl 1072.54006

Fang, Jinming; Yue, Yueli

Inf. Sci. 162, No. 3-4, 139-146 (2004).

The authors give a new definition of connectivity in a fuzzifying topological space and generalize a known theorem of K. Fan to their setting [Fan’s theorem says that a topological space \(X\) is connected iff for any \(a\), \(b\) of \(X\), there is a finite subset \(\{x_1,x_2,\dots, x_n\}\) of \(X\) such that \(x_1= a\), \(x_2= b\) and \(N(x_i)\cap N(x_{i+1})\neq\phi\), for \(i= 1,2,\dots, n-1\), where \(N: X\to\wp(X)\) such that \(N(x)\) is neighbourhood of \(x\) for all \(x\in X\)].

Reviewer: M. N. Mukherjee (Calcutta)

MSC:

54A40	Fuzzy topology
03B50	Many-valued logic
54D05	Connected and locally connected spaces (general aspects)

Keywords:

Łukasiewicz logic; Topology; Fuzzifying topology; Connectivity

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