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Best approximation in fuzzy metric spaces. (English) Zbl 0986.54006
The structure studied in the paper is the fuzzy metric space (a modified definition of the statistical metric space), which is a triple $$(X, M, *)$$, where $$X$$ is the universe, $$*$$ is a triangular norm and $$M:X^2 \times (0, \infty) \to [0,1]$$ with properties usual for fuzzy metric spaces. Special attention is given to strong fuzzy metric spaces, i.e. spaces, where $$M$$ is continuous in its first variable. Problems of best approximation are studied in these spaces. The author describes the closure of a set in terms of $$M$$ and proves the theorem on the existence of best approximation.

##### MSC:
 54A40 Fuzzy topology
##### Keywords:
fuzzy metric space