Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SPACE OF HOMEOMORPHISMS UNDER REGULAR TOPOLOGY

  • Mir Aaliya (Department of Mathematics Lovely Professional University) ;
  • Sanjay Mishra (Department of Mathematics Lovely Professional University)
  • Received : 2022.12.05
  • Accepted : 2023.03.14
  • Published : 2023.10.31
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Abstract

In this paper, we attempt to study several topological properties for the function space H(X), 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 H(X) 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.

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References

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