Reflexive extended locally convex spaces
Akshay Kumar, Varun Jindal

TL;DR
This paper investigates the reflexivity of extended locally convex spaces using the topology of uniform convergence on bounded sets, establishing conditions under which reflexivity is preserved in subspaces and extended normed spaces.
Contribution
It introduces the use of the topology b to analyze reflexivity in extended locally convex spaces, showing reflexivity is a three-space property for extended normed spaces.
Findings
Reflexivity of elcs is equivalent to all open subspaces being reflexive.
Reflexivity is a three-space property in extended normed spaces.
The topology b is effective for studying reflexivity in these spaces.
Abstract
For an extended locally convex space (elcs) , the authors in [10] studied the topology of uniform convergence on bounded subsets of on the dual of . In the present paper, we use the topology to explore the reflexive property of extended locally convex spaces. It is shown that an elcs is (semi) reflexive if and only if any of its open subspaces is (semi) reflexive. For an extended normed space, we show that reflexivity is a three-space property.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Fixed Point Theorems Analysis · Optimization and Variational Analysis
