# Selection principles and games in bitopological function spaces

## TL;DR

This paper investigates selective properties and topological games in the space of continuous functions on a Tychonoff space, focusing on the interplay between compact-open and pointwise convergence topologies.

## Contribution

It extends the study of selective separability and tightness by analyzing new variations of these properties and associated topological games in bitopological function spaces.

## Key findings

- Analysis of selective properties in $(C(X), \tau_k, \tau_p)$
- Development of topological game frameworks for these spaces
- Identification of conditions affecting separability and tightness

## Abstract

For a Tychonoff space $X$, we denote by $(C(X), \tau_k, \tau_p)$ the bitopological space of all real-valued continuous functions on $X$ where $\tau_k$ is the compact-open topology and $\tau_p$ is the topology of pointwise convergence. In papers [5, 6, 13] variations of selective separability and tightness in $(C(X), \tau_k, \tau_p)$ were investigated. In this paper we continued to study the selective properties and the corresponding topological games in the space $(C(X), \tau_k, \tau_p)$.