Wallman compactification

**Wallman compactification** is a particular compactification of $T_1$-topological spaces introduced in

- Henry Wallman,
*Lattices and topological spaces*, Annals of Math.**39**:1 (Jan., 1938), pp. 112-126 jstor

There are recent applications related to topoi and noncommutative geometry

- Olivia Caramello,
*Gelfand spectra and Wallman compactifications*, arxiv/1204.3244;*Dualité de Gelfand et bases de Wallman*, seminar talk videos

A **Wallman base** $B$ for a topological space $X$ is a sublattice of of the frame $Open(X)$ of open sets of $X$ which is a base for the topology and satisfies the property that for any $U\in B$ and $x\in U$ there exists $V\in B$ such that $U\cup V = X$ and $x\notin V$.

Standard references are

- P. T. Johnstone,
*Stone Spaces*, Cambridge Studies in Advanced Math.**3**(1982). - [eom]: Wallman compactification
- wikipedia: Wallman compactification

category: topology

Created on April 24, 2013 at 19:15:14. See the history of this page for a list of all contributions to it.