Generalizing Topology via Chu Spaces

TL;DR

This paper introduces generalized topological spaces (GTS) using Chu spaces, extending classical topology, and interprets linear logic connectives as operators on these spaces, unifying topology and logic.

Contribution

It defines GTS via Chu spaces, broadening the concept of topology and linking it with linear logic through a novel interpretative framework.

Findings

GTS generalizes classical topological spaces

Linear logic connectives are interpreted as topological operators

GTS encompasses known topological spaces as special cases

Abstract

By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these topological spaces have as special cases known topological spaces. Furthermore, we develop the various topological notions and concepts for GTS. Moreover, since the logic of Chu spaces is linear logic, we give an interpretation of most linear logic connectives as operators that yield topological spaces.