RMC - Vol. 10, Num. 1 - Manuel Valdivia

Full paper in PDF:
$%M. Valdivia, On certain compact topological spaces, Rev. Mat. Univ. Complut. Madrid 10 (1997), no. 1, 81–84.%$

On Certain Compact Topological Spaces

Manuel VALDIVIA

Departamento de Análisis Matemático
Universidad de Valencia
Dr. Moliner 50
46100 Burjasot (Valencia) — Spain

Received: April 24, 1996
Revised: October 10, 1996

ABSTRACT

A compact topological space $K$ is in the class $A$ if it is homeomorphic to a subspace $H$ of $[0,1]I$ , for some set of indexes $I$ , such that, if $L$ is the subset of $H$ consisting of all ${xi :i (- I}$ with $xi =0$ except for a countable number of $i$ ’s, then $L$ is dense in $H$ . In this paper we show that the class $A$ of compact spaces is not stable under continuous maps. This solves a problem posed by Deville, Godefroy and Zizler.

1991 Mathematics Subject Classification: 54D30.