Monomorphisms in spaces with Lindel\"of filters via some compact-open-like topologies on C(X)

TL;DR

This paper characterizes monomorphisms in the category of spaces with Lindelöf filters by introducing new compact-open-like topologies on the space of continuous functions, extending previous criteria.

Contribution

It extends existing criteria for monomorphisms in LSpFi and introduces new topologies on C(X) to characterize these monomorphisms.

Findings

Extended the criterion for monomorphisms in LSpFi.

Defined new compact-open-like topologies on C(X).

Provided new characterizations of monomorphisms using these topologies.

Abstract

We study the monomorphisms in the category LSpFi of spaces with Lindel\"{o}f Filters. We extend the criterion derived by R. Ball and A. Hager in "Monomorphisms in Spaces with Lindel\"{o}f Filters", Czech. Math.J. 57, No.1 (2007) 281-317. Based on this extension, we defined and studied some compact-open-like topologies on C(X) and give new characterizations of the monomorphisms in LSpFi via these topologies.