On the topology of n-normed spaces with respect to norms of its quotient spaces
Batkunde H.a, Gunawan H.a
a Analysis and Geometry Group, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, 40132, Indonesia
Abstract
© 2019 SAE International. All rights reserved.In this paper, we study some topological characteristics of n-normed spaces. We construct quotient spaces of an n-normed space and define a norm in each quotient space. Using these norms, we observe convergence sequences, closed sets, and bounded sets in n-normed spaces. These norms will be a new viewpoint in observing the characteristics of n-normed spaces. We also review the completeness of n-normed spaces.
Author keywords
Indexed keywords
Bounded set,Closed set,Completeness,N-normed space