Valdivia, M. On certain compact topological spaces. (English) Zbl 0870.54025 Rev. Mat. Univ. Complutense Madr. 10, No. 1, 81-84 (1997). Summary: A compact topological space \(K\) is in the class \({\mathcal A}\) 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 \(\{x_i:i\in I\}\) with \(x_i=0\) except for a countable number of \(i\)’s, then \(L\) is dense in \(H\). In this paper we show that the class \({\mathcal A}\) of compact spaces is not stable under continuous maps. This solves a problem posed by R. Deville, G. Godefroy and V. Zizler [Smoothness and renormings in Banach spaces (1993; Zbl 0782.46019)]. Cited in 2 Reviews MSC: 54D30 Compactness Citations:Zbl 0782.46019 PDFBibTeX XMLCite \textit{M. Valdivia}, Rev. Mat. Univ. Complutense Madr. 10, No. 1, 81--84 (1997; Zbl 0870.54025) Full Text: EuDML