Strong \(\beta\)-spaces and their countable products. (English) Zbl 1243.54046

Summary: We introduce a new concept called “strong beta-spaces”. Strong beta-spaces are beta-spaces. Semi-stratifiable spaces, strong Sigma-spaces and strict \(p\)-spaces are all strong beta-space. Thus, the class of strong beta-spaces is well located in the classes of generalized metric spaces. This class does not coincide with the class of beta-spaces, but they coincide under the condition of paracompactness. As a merit of the class of strong beta-spaces, we show that it is countably productive. Moreover, it is shown that the class of normal strong beta-spaces (or paracompact beta-spaces) is countably productive if it is finitely productive.


54E20 Stratifiable spaces, cosmic spaces, etc.
54B10 Product spaces in general topology
54E18 \(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.