• Communications of the Korean Mathematical Society
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• v.37 no.3
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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
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• v.9 no.2
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• pp.381-388
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• 1993

• Journal of the Korean Mathematical Society
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• v.13 no.2
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• pp.155-159
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• 1976

• The Mathematical Education
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• v.17 no.1
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• pp.81-83
• /
• 1978

• The Mathematical Education
• /
• v.13 no.2
• /
• pp.24-26
• /
• 1974

• The Mathematical Education
• /
• v.16 no.1
• /
• pp.35-38
• /
• 1977

• Communications of the Korean Mathematical Society
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• v.38 no.4
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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.