nLab
locally compact locale

Contents

Definition

A locale is locally compact if its frame of opens is a continuous poset.

Properties

Proposition

In classical mathematics, every locally compact locale is spatial, hence may be regarded as a locally compact topological space.

Remark

Prop. may fail in constructive mathematics. For instance any spectrum of a commutative ring, considered as a locale, is locally compact, but may fail to be spatial (because of the lack of filters).

Propsition

Locally compact locales are also exactly the exponentiable objects in the category of locales.

Last revised on May 3, 2017 at 03:42:15. See the history of this page for a list of all contributions to it.