nLab locally connected locale

Redirected from "locally connected locales".
Note: locally connected locale, locally connected locale, and locally connected locale all redirect for "locally connected locales".

Definition

A locale $L$ is connected if $1\ne0$ and $1=A\cup B$ for disjoint opens $A$ and $B$ implies $A=0$ or $B=0$ .

A locale $L$ is locally connected if its connected opens form a base (any open is a supremum of connected opens).

For a locally connected locale one can define its set of connected components.

See cosheaf of connected components for a parametrized version of this construction.

Created on April 18, 2020 at 21:50:26. See the history of this page for a list of all contributions to it.