Spaces of Compact Open Subgroups and Open Morphisms
Year: 2026
Type: article
Abstract: For a morphism whose domain is a totally disconnected locally compact group, the openness test of Cowling, Hofmann and Morris [‘Open mappings of locally compact groups’, J. Group Theory 27 (6) (2024), 1143–1149] can be stated in terms of compact open subgroups. We use this formulation to study spaces of compact open subgroups. A surjective open morphism with compact kernel induces a quotient map between such spaces, and the inverse-image map identifies the target with a closed retract of the source. Conversely, for a surjective open morphism whose target has a compact open subgroup, compactness of the kernel is forced by the requirement that inverse images of compact open subgroups remain compact.
Authors: XING-YU HU, RAN WEN
Institutions: Hanjiang Normal University, Xinjiang Hetian College
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,550
OpenAlex ID: W7208716479