Bounded Sets in Topological Spaces
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadata
Title
Bounded Sets in Topological SpacesDate
2022-02Publisher
MDPIISSN
2075-1680Bibliographic citation
Bors, C.; Ferrer, M.V.; Hernández, S. Bounded Sets in Topological Spaces. Axioms 2022, 11, 71. https://doi.org/10.3390/axioms11020071Type
info:eu-repo/semantics/articlePublisher version
https://www.mdpi.com/2075-1680/11/2/71Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is said to be G-bounded if for each neighbourhood U of ... [+]
Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is said to be G-bounded if for each neighbourhood U of x0 there is a finite subset F of G with A⊆FU. We prove that for a metrizable and separable G-space X, the bounded subsets of X are completely determined by the bounded subsets of any dense subspace. We also obtain sufficient conditions for a G-space X to be locally G-bounded, which apply to topological groups. Thereby, we extend some previous results accomplished for locally convex spaces and topological groups. [-]
Is part of
Axioms. 2022; 11(2): 71Funder Name
Ministerio de Economía y Competitividad | Universitat Jaume I
Project code
MTM/PID2019-106529GB-I00 | UJI-B2019-06
Rights
info:eu-repo/semantics/openAccess
This item appears in the folowing collection(s)
- INIT_Articles [751]
- MAT_Articles [761]