The boundary of an open convex set in a topological module
Abstract
Abstract In classical Banach Space Theory, it is well known that the unit sphere can be seen as a slice of the closed unit ball by the norm, which is weakly lower semicontinuous. Later on, this classical result was extended to a more general setting by proving that the boundary of a nonempty proper open convex subset of a real topological vector space can be obtained via the slice of its closure by a convenient lower semicontinuous convex function. In this manuscript, this is taken one step further since the boundary of a nonempty proper open convex subset of a topological module over a topological ordered ring is proved to be the slice of its closure by a certain lower semicontinuous convex function.
Fields of Study & Subjects
Optimization and Variational Analysis
Advanced Banach Space Theory
Fixed Point Theorems Analysis
Publication details
- Journal / source
- The Journal of Analysis
- Volume
- 34
- Issue
- 1
- Pages
- 217–228
- Publication date
- 8 January 2026
- Language
- EN