The C-compact-open topology on function spaces

TL;DR

This paper explores the properties of the C-compact-open topology on continuous function spaces, comparing it with other topologies and analyzing conditions for metrizability, separability, and second countability.

Contribution

It provides a comprehensive analysis of the C-compact-open topology, including its metrizability, submetrizability, separability, and second countability, and compares it with other known topologies.

Findings

C-compact-open topology can be metrizable under certain conditions

The topology is submetrizable and separable in specific cases

Conditions for second countability are characterized

Abstract

This paper studies the C-compact-open topology on the set C(X) of all realvalued continuous functions on a Tychonov space X and compares this topology with several well-known and lesser known topologies. We investigate the properties C-compact-open topology on the set C(X) such as submetrizable, metrizable, separable and second countability.