Lion and man in non-metric spaces

TL;DR

This paper explores the strategic possibilities of a lion and a man moving continuously in a general topological space, extending previous studies from metric spaces to more abstract topological settings.

Contribution

It generalizes the problem of pursuit and evasion strategies from metric spaces to arbitrary topological spaces, broadening the theoretical framework.

Findings

Analysis of pursuit-evasion strategies in topological spaces

Extension of classical results to non-metric contexts

Identification of conditions for strategy existence

Abstract

A lion and a man move continuously in a space $X$. The aim of the lion is to capture his prey while the man wants to escape forever. Which of them has a strategy? This question has been studied for different metric domains. In this article we consider the case of general topological spaces.