Topological structure of 2-normed space and some results in linear 2-normed spaces analogous to baire’s theorem and banach Steinhaus theorem

P. Riyas
Department of Mathematics, K M M Govt.Women’s College, Kannur, India-670004.
K. T. Ravindran
P G Departmentof Mathematics, Payyannur College, Kannur, India-670627.

\(^{1}\)Corresponding Author: riyasmankadavu@gmail.com

Copyright © 2014 P. Riyas, K. T. Ravindran. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2014.

Abstract

In this paper we construct the topological structure of linear 2-normed space. This enable us to define the concept of open sets in linear 2-normed space and derive an analogue of Baire’s theorem and Banach Steinhaus theorem in linear 2-normed spaces.

Keywords:

linear 2-normed space, locally convex topological vector space, 2-Banach space, equi-continuity, locally bounded set, equi-bounded.