1Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.
2Departamento de estadistica ymatem'atica aplicada, universidad de almeria, e-04120, Spain
3Department of Mathematics Iran University of Science and Technology, Narmak, Tehran, Iran.
The notion of a probabilistic metric space corresponds to the situations when we do not know exactly the distance. Probabilistic Metric space was introduced by Karl Menger. Alsina, Schweizer and Sklar gave a general definition of probabilistic normed space based on the definition of Menger . In this note we study the PN spaces which are topological vector spaces and the open mapping and closed graph Theorems in this spaces are proved.