Document Type : Research Paper

Authors

• M. B. Ghaemi ¹
• L. Guillen ²
• S. Saiedinezhad ³

¹ Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran.

² Departamento de Estadistica Ymatem'atica Aplicada, Universidad de Almeria, e-04120, Spain

³ Department of Mathematics Iran University of Science and Technology, Narmak, Tehran, Iran.

Abstract

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 [1]. 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.

Keywords

• continuous linear map
• homomorphism
• Triangular function
• topological vector space