Resumen de Strong beta-spaces and their countable products

Yukinobu Yajima

• 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.