A note on the category of c-spaces

TL;DR

This paper demonstrates that the category of c-spaces, and consequently locally finitary compact spaces, lack the property of being cartesian closed, impacting their use in certain mathematical and computational contexts.

Contribution

It establishes that the category of c-spaces is not cartesian closed, providing insight into the structural limitations of these spaces.

Findings

Category of c-spaces is not cartesian closed

Locally finitary compact spaces also lack cartesian closure

Implications for mathematical and computational frameworks

Abstract

We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not cartesian closed.