Some properties of continuous linear operators in topological vector PN-spaces

Abstract

The notion of a probabilistic metric space corresponds to the<br />situations when we do not know exactly the<br /> distance. Probabilistic Metric space was<br /> introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of<br /> probabilistic normed space based on the definition of Menger [1]. In this note we study the PN spaces which are<br /> topological vector spaces and the open mapping and closed graph<br /> Theorems in this spaces are proved.