A characterization of metrizable finitistic spaces and its applications to upper semicontinuous set-valued selections

• Autores: Takamitsu Yamauchi
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 33, Nº 3, 2007, págs. 735-751
• Idioma: inglés
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• Resumen

  • In this paper, we give two types of characterizations of finitistic spaces. One is in terms of perfect mappings from zero-dimensional metric spaces, which is analogous to K. Morita's characterization of finite-dimensional metrizable spaces. Another is by means of upper semicontinuous set-valued selections, which is an analogue of M. M. Coban's characterization of finite-dimensional paracompact spaces. Characterizations of some classes of infinite-dimensional spaces and a generalization of finitistic spaces will also be given.