Strong beta-spaces and their countable products

• Autores: Yukinobu Yajima
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 2, 2007, págs. 531-540
• Idioma: inglés
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• Resumen

  • 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.