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 C 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.
@article{urn:eudml:doc:44244,
title = {On certain compact topological spaces.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {10},
year = {1997},
pages = {81-84},
zbl = {0870.54025},
mrnumber = {MR1452564},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44244}
}
Valdivia, Manuel. On certain compact topological spaces.. Revista Matemática de la Universidad Complutense de Madrid, Tome 10 (1997) pp. 81-84. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44244/