Cofinitely and co-countably projective spaces


  • Pablo Mendoza Iturralde Instituto Politécnico Nacional
  • Vladimir V. Tkachuk Universidad Autónoma Metropolitana



Cofinitely projective, Co-countably projective, Scattered compact


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.


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Author Biographies

Pablo Mendoza Iturralde, Instituto Politécnico Nacional

Departamento de Ciencias Básicas. Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas

Vladimir V. Tkachuk, Universidad Autónoma Metropolitana

Departamento de Matemáticas




How to Cite

P. Mendoza Iturralde and V. V. Tkachuk, “Cofinitely and co-countably projective spaces”, Appl. Gen. Topol., vol. 3, no. 2, pp. 185–195, Oct. 2002.



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