Space of homeomorphisms under regular topology
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In this paper, we attempt to study several topological properties for the function space $\hx$, space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at $X$ compact. Furthermore, we prove that the space $\hx$ endowed with the regular topology is a topological group when $X$ is a metric, almost $P$-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on $\R$ under regular topology are open subspaces of $H(\R)$ and are homeomorphic.
Abstract
In this paper, we attempt to study several topological properties for the function space $\hx$, space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at $X$ compact. Furthermore, we prove that the space $\hx$ endowed with the regular topology is a topological group when $X$ is a metric, almost $P$-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on $\R$ under regular topology are open subspaces of $H(\R)$ and are homeomorphic.
참고문헌 (9)
- M. Aaliya, "Some properties of regular topology on C(X, Y )", Itl. J. Pure Appl. Math. (2022)
- M. Aaliya, "Compactness and cardinality of the space of continuous functions under regular topology", ~ (2022)
- R. F. Arens, "Topologies for homeomorphism groups", Amer. J. Math, 68, pp.593~610 (1946)[DOI]
- J. J. Dijkstra, "On homeomorphism groups and the compact-open topology", Amer. Math. Monthly, 112(10), pp.910~912 (2005)[DOI]
- W. Iberkleid, "The regular topology on C(X)", Comment. Math. Univ. Carolin, 52(3), pp.445~461 (2011)
- A. Jindal, "The regular topology on C(X, Y )", Acta Math. Hungar, 158(1), pp.1~16 (2019)[DOI]
- R. A. McCoy, "Topological homeomorphism groups and semi-box product spaces", Topology Proc, 36, pp.267~303 (2010)
- R. A. McCoy, "Homeomorphism spaces under uniform and fine topologies", Houston J. Math, 39(3), pp.1051~1066 (2013)
- R. A. McCoy, "Function Spaces with Uniform, Fine and Graph Topologies, Springer Briefs in Mathematics" (2018), Springer