Cofinitely and co-countably projective spaces

Authors

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

DOI:

https://doi.org/10.4995/agt.2002.2062

Keywords:

Cofinitely projective, Co-countably projective, Scattered compact

Abstract

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.

Downloads

Download data is not yet available.

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

Downloads

Published

2002-10-01

How to Cite

[1]
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.

Issue

Section

Regular Articles