# Topological games of bounded selections

## TL;DR

This paper introduces a new class of topological selection principles and associated games that interpolate between classical properties, revealing novel topological behaviors in covering and tightness contexts.

## Contribution

It proposes a new variation of classical selection principles and topological games, expanding the framework for analyzing topological properties.

## Key findings

- New selection principles between existing ones
- Emergence of novel topological properties
- Application to covering and tightness scenarios

## Abstract

We present a new variation of the classical selection principles $\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$ ($k\in\mathbb N$) and $\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$ that formally lies between these two properties. As in the case of the classical selection principles, we also obtain a new variation of topological games and discuss how new topological properties may emerge in the specific cases of covering and tightness.