nLab positive locale

Contents

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

Definition

An open sublocale O∈π’ͺ(L)O \in \mathcal{O}(L) is positive if, whenever OO is the indexed join of open sublocales U i∈π’ͺ(L)U_i \in \mathcal{O}(L)

O=⋁ i:IU iO = \bigvee_{i:I} U_i

the index set II is inhabited.

A locale LL is positive if the top open sublocale L∈π’ͺ(L)L \in \mathcal{O}(L) is positive.

See also

References

Created on June 1, 2022 at 09:31:39. See the history of this page for a list of all contributions to it.