TY - JOUR
AU - Mendoza Iturralde, Pablo
AU - Tkachuk, Vladimir V.
PY - 2002/10/01
Y2 - 2024/02/28
TI - Cofinitely and co-countably projective spaces
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 3
IS - 2
SE -
DO - 10.4995/agt.2002.2062
UR - https://polipapers.upv.es/index.php/AGT/article/view/2062
SP - 185-195
AB - <p>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 â”‚X\Uâ”‚ ≤ 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.</p>
ER -