nLab sigma-locale

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents

Idea

 Definition

A σ\sigma-locale consists of a set XX with a sigma-frame 𝒪(X)\mathcal{O}(X).

A continuous function f:XYf:X \to Y between σ\sigma-locales XX and YY is a sigma-frame homomorphism f *:𝒪(Y)𝒪(X)f^*:\mathcal{O}(Y) \to \mathcal{O}(X), a monotonic function which preserves finite meets and countable joins.

 References

Last revised on August 30, 2024 at 13:49:21. See the history of this page for a list of all contributions to it.