The finest locally convex topology of an extended locally convex space

2022/07/31 by Akshay Kumar, Kumar, Akshay, Varun Jindal +1
Computer Science · Mathematics · #46A03 #46A17 #46A20 #46B20 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #General Topology (math.GN) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2208.00389

openalex publication_date 2022/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Salas and Garcia introduced the concept of an extended locally convex space in [D. Salas and S. Tapia-Garcia. Extended seminorms and extended topological vector spaces. Topology and its Applications, 2016] which extends the idea of an extended normed space (introduced by Beer in G. Beer. Norms with infinite values. Journal of Convex Analysis, 2015). This article gives an attractive formulation of the finest locally convex topology of an extended locally convex space and provides a systematic study of the resulting locally convex space. As an application, we characterize the coincidence of the finest locally convex topologies corresponding to the topologies of uniform and strong uniform convergences on a bornology for the function space C(X).

Related

• Dual of an extended locally convex space
• Barreled extended locally convex spaces and Uniform boundedness principle
• Reflexive extended locally convex spaces
• ω^ω-Base and infinite-dimensional compact sets in locally convex spaces
• Locally convex spaces with the strong Gelfand-Phillips property