nLab
locally connected locale

Definition

A locale LL is connected if 101\ne0 and 1=AB1=A\cup B for disjoint opens AA and BB implies A=0A=0 or B=0B=0.

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

Properties

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 17:50:26. See the history of this page for a list of all contributions to it.