• 대한수학회논문집
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• 제37권3호
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• East Asian mathematical journal
• /
• 제9권2호
• /
• pp.381-388
• /
• 1993

• 대한수학회지
• /
• 제13권2호
• /
• pp.155-159
• /
• 1976

• 한국수학교육학회지시리즈A:수학교육
• /
• 제17권1호
• /
• pp.81-83
• /
• 1978

• 한국수학교육학회지시리즈A:수학교육
• /
• 제13권2호
• /
• pp.24-26
• /
• 1974

• 한국수학교육학회지시리즈A:수학교육
• /
• 제16권1호
• /
• pp.35-38
• /
• 1977

• 대한수학회논문집
• /
• 제38권4호
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• pp.1299-1307
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• 2023

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.