Nagata Spaces and wN-spaces which are preserved by Quasi-Perfect Maps

• Autores: Shin-ichi Nitta, Iwao Yoshioka
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 32, Nº 4, 2006, págs. 1061-1076
• Idioma: inglés
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• Resumen

  • G.Ying and C.Good (2001) described that Lutzer's example (1971) asserts that neither Nagata spaces nor wN-spaces are necessarily preserved under quasi-perfect maps. We introduce some classes of spaces which are contained in the class of wN-spaces and show that these classes are invariant under quasi-perfect maps or closed almost-open maps, but not preserved by closed map nor open finite-to-one maps. We also show that in the realm of paracompact spaces, these new classes coincide with the class of M-spaces in the sense of Morita, and study conditions for metrizability of these classes.