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

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 $$x\in X$$].

### 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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### References:

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