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February 25, 2026Journal of Group Theory0 citations

On continuity of group-valued mappings with respect to Chabauty topology

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NANejeh Alaya

Key Points

  • This research aims to determine necessary and sufficient conditions for continuity of specific group-valued mappings.
  • Defined the set of closed subgroups equipped with the Chabauty topology.
  • Analyzed mappings from a topological space to this set of closed subgroups.
  • Established mathematical conditions related to continuity.
  • Provided conditions that characterize the continuity of the mapping.
  • Described implications of continuity in relation to the structure of locally compact groups.

Abstract

Abstract Let 𝐺 be a locally compact group and let S ⁢ U ⁢ B ⁢ (G) SUB (G) be the set of closed subgroups of 𝐺 equipped with the Chabauty topology. In this paper, we establish some necessary and sufficient conditions for a map T: X → S ⁢ U ⁢ B ⁢ (G) T X (G), from a topological space 𝑋 into S ⁢ U ⁢ B ⁢ (G) SUB (G), to be continuous.

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Cite This Study

Nejeh Alaya (2026) studied this question.

synapsesocial.com/papers/699e9143f5123be5ed04ea83https://doi.org/10.1515/jgth-2025-0038
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