The Chabauty and the Thurston topologies on the hyperspace of closed subsets

研究成果: Article査読

1 被引用数 (Scopus)

抄録

For a regularly locally compact topological space X of T0 separation axiom but not necessarily Hausdorff, we consider a map σ from X to the hyperspace C(X) of all closed subsets of X by taking the closure of each point of X. By providing the Thurston topology for C(X), we see that σ is a topological embedding, and by taking the closure of σ(X) with respect to the Chabauty topology, we have the Hausdorff compactification X̂ of X. In this paper, we investigate properties of X̂ and C(X̂) equipped with different topologies. In particular, we consider a condition under which a self-homeomorphism of a closed subspace of C(X) with respect to the Chabauty topology is a self-homeomorphism in the Thurston topology.

本文言語English
ページ(範囲)263-292
ページ数30
ジャーナルJournal of the Mathematical Society of Japan
69
1
DOI
出版ステータスPublished - 2017

ASJC Scopus subject areas

  • Mathematics(all)

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