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The weak topology in finite dimensional asymmetric normed spaces
- Source :
- RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia, instname
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- [EN] In this paper we show that, in contrast to what happens in a normed space, the weak topology of a finite dimensional asymmetric normed space is not necessarily the same as the topology of the asymmetric norm. We provide a class of finite dimensional asymmetric normed spaces where both topologies coincide. We also prove that the weak topology of an infinite dimensional asymmetric normed space is strictly coarser than the topology of the asymmetric norm. (C) 2019 Elsevier B.V. All rights reserved.
- Subjects :
- Asymmetric lattice norm
Pure mathematics
Class (set theory)
Weak topology
Asymmetric norm
010102 general mathematics
Network topology
01 natural sciences
010101 applied mathematics
Geometry and Topology
0101 mathematics
MATEMATICA APLICADA
Topology (chemistry)
Semicontinuous function
Normed vector space
Mathematics
Subjects
Details
- ISSN :
- 01668641
- Volume :
- 264
- Database :
- OpenAIRE
- Journal :
- Topology and its Applications
- Accession number :
- edsair.doi.dedup.....b91c648305f7c0e8baa421768b2d6615