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

Document Type : Research Paper

Authors

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

Volume 1, Issue 1 - Serial Number 1
January 2010
Pages 58-64
  • Receive Date: 11 March 2009
  • Revise Date: 26 September 2013
  • Accept Date: 02 October 2013
  • First Publish Date: 02 October 2013