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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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