TY - JOUR

T1 - On the extent of star countable spaces

AU - Alas, O.T.

AU - Junqueira, L.R.

AU - van Mill, J.

AU - Tkachuk, V.V.

AU - Wilson, R.G.

PY - 2011

Y1 - 2011

N2 - For a topological property P, we say that a space X is star P if for every open cover U of the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω

AB - For a topological property P, we say that a space X is star P if for every open cover U of the space X there exists Y ⊂ X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelöf spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelöf. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense σ-compact subspace can have arbitrary extent. It is proved that for any ω

U2 - 10.2478/s11533-011-0018-y

DO - 10.2478/s11533-011-0018-y

M3 - Article

SP - 603

EP - 615

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

SN - 1895-1074

ER -