Productively countably tight spaces of the form C_k(X)

TL;DR

This paper explores conditions under which the space of continuous real functions with the compact-open topology is productively countably tight, using bornologies, and discusses applications to Alster spaces.

Contribution

It introduces new conditions involving bornologies that determine when C_k(X) is productively countably tight, advancing understanding in C_k-theory.

Findings

Identifies conditions for C_k(X) to be productively countably tight

Provides applications to the theory of Alster spaces

Advances the use of bornologies in C_k-theory

Abstract

Some results in C_k-theory are obtained with the use of bornologies. We investigate under which conditions the space of the continuous real functions with the compact-open topology is a productively countably tight space, which yields some applications on Alster spaces.