Cofinitely and co-countably projective spaces
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Mendoza Iturralde, Pablo [1] ; Tkachuk, Vladimir V. [2]
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[1] Instituto Politécnico Nacional
Instituto Politécnico Nacional
México
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[2] Universidad Autónoma Metropolitana
Universidad Autónoma Metropolitana
México
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- Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 3, Nº. 2, 2002, págs. 185-195
- Idioma: inglés
- DOI: 10.4995/agt.2002.2062
- Enlaces
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Resumen
We show that X is cofinitely projective if and only if it is a finite union of Alexandroff compactatifications of discrete spaces. We also prove that X is co-countably projective if and only if X admits no disjoint infinite family of uncountable cozero sets. It is shown that a paracompact space X is co-countably projective if and only if there exists a finite set B C X such that B C U ϵ τ (X) implies │X\U│ ≤ ω. In case of existence of such a B we will say that X is concentrated around B. We prove that there exists a space Y which is co-countably projective while there is no finite set B C Y around which Y is concentrated. We show that any metrizable co-countably projective space is countable. An important corollary is that every co-countably projective topological group is countable.
