Pretopologies, preuniformities and probabilistic metric spaces (Q2495667)

The authors investigate several interesting relations between pretopologies, preuniformities and probabilistic metric spaces. They establish that the family of filters inducing a given pretopology form a complete lattice. The largest element of this lattice is characterized similarly to the construction used by \textit{B. Knaster, C. Kuratowski} and \textit{S. Mazurkiewicz} in [Fundam. Math. 14, 132--137 (1929; JFM 55.0972.01)]. Some properties of pretopologies and probabilistic metric spaces are obtained.