Journal of Prime Research in Mathematics

# 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

### 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.