Subspaces of the Space of Real-Valued Continuous Functions Endowed with Regular Topology

Authors

• Mir Aaliya, Government Degree College for Boys
• Sanjay Mishra, Amity University

Abstract

This paper studies the regular topology and its relation with the point-open topology and the graph topology on the function space C(X), where X is a Tychonoff space. Furthermore, it characterizes different subspaces of the function space C(ℝ) endowed with regular topology and few more results corresponding to the regular topology on C(X). Moreover, it is proved that the graph topology is stronger than the regular topology and they coincide when X is a weak cb-space, for the function space C(X).

Publication Title

Boletim Da Sociedade Paranaense De Matematica

Recommended Citation

Mir Aaliya., & Mishra, S. (2025). Subspaces of the Space of Real-Valued Continuous Functions Endowed with Regular Topology. Boletim Da Sociedade Paranaense De Matematica, 43 https://doi.org/10.5269/bspm.63975