IJPAM: Volume 81, No. 4 (2012)

WALLMAN COMPACTIFICATIONS ARE
PRE-UNIFORM COMPLETIONS

Adalberto García-Máynez Cervantes$^1$, Rubén Santos Mancio Toledo$^2$
$^1$Instituto de Matemáticas
Universidad Nacional Autónoma de México
Area de la Investigación Cientıfica
Circuito Exterior, Ciudad Universitaria. México D.F. C.P. 04510
$^2$Escuela Superior de Física y Matemáticas del Instituto
Politécnico Nacional
Edificio No. 9, Unidad Profesional Adolfo López Mateos
Colonia Lindavista, México D.F. C.P. 07738


Abstract. We prove that every Wallman compactifications of a $\mathrm{T}_{1}$-space $\left(X,\tau\right)$ may be viewed as the completion of certain pre-uniform space $\left(X,\mathcal{U}\right)$, where $\mathcal{U}$ is a precompact pre-uniform basis compatible with $\tau$. We also study perfect extensions of pre-uniform spaces.

Received: May 20, 2011

AMS Subject Classification: 54A05, 54A20, 54E15

Key Words and Phrases: Wallman compactification, pre-uniformity basis, weakly round filter, perfect extension, mingling filters

Download paper from here.


Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 4