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\(\tau\)-distance in a general topological space \((X,\tau)\) with application to fixed point theory. (English) Zbl 1051.54027
Summary: The main purpose of this paper is to define the notion of a \(\tau\)-distance function in a general topological space \((X,\tau)\). As application, we get a generalization of the well-known Banach fixed point theorem.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
54A05 Topological spaces and generalizations (closure spaces, etc.)
47H10 Fixed-point theorems
54E70 Probabilistic metric spaces
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