A Note on the Open Mappings of Locally Compact Groups
Year: 2025
Type: article
Abstract: Let G be a locally compact topological group and script upper L left parenthesis upper G right parenthesis $\mathcal {L}(G)$ L ( G ) the space of all its closed subgroups endowed with the Vietoris topology. Let upper L Subscript c Baseline left parenthesis upper G right parenthesis $\mathcal {L}_c(G)$ L c ( G ) be the subspace of all compact subgroups of G . Any continuous morphism phi colon upper G right arrow upper H $\varphi \colon G\to H$ φ : G → H between locally compact groups G and H functorially induces a continuous map phi Subscript asterisk Baseline colon upper L Subscript c Baseline left parenthesis upper G right parenthesis right arrow upper L Subscript c Baseline left parenthesis upper H right parenthesis $\varphi _*\colon \mathcal {L}_c(G)\to \mathcal {L}_c(H)$ φ ∗ : L c ( G ) → L c ( H ) given by phi Subscript asterisk Baseline left parenthesis upper L right parenthesis equals phi left parenthesis upper L right parenthesis $\varphi _*(L)=\varphi (L)$ φ ∗ ( L ) = φ ( L ) . The main problem addressed in this paper is that of determining the relationship between the openness of phi
Author: ZOUHOUR JLALI
Institutions: University of Sfax, Faculty of Sciences of Sfax
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W4416102541