On products of certain D-spaces

• Autores: Liang-Xue Peng
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 34, Nº 1, 2008, págs. 165-180
• Idioma: inglés
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• Resumen

  • D--spaces were introduced by van Douwen in 1978 and studied by van Douwen and many other topologists. It is not yet clear which topological spaces are D-spaces, and the product theory for D-spaces is not yet complete. In this paper we use certain topological games of Galvin to obtain any countable product of paracompact DC--like spaces is a D-space, and consequently that any countable product of paracompact C-scattered spaces is a D-space. We also show that a special generalized metric space is a D-space, this result extends results of R. Z. Buzyakova. For a fixed integer n, any box product of scattered spaces each with a scattered rank n must be a D-space. The last conclusion extands results of William G. Fleissner and Adrienne M. Stanley