On spaces in which countably compact sets are closed, and hereditary properties |
| |
Authors: | Mohammad Ismail |
| |
Institution: | Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA;Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA |
| |
Abstract: | A space X is called C-closed if every countably compact subset of X is closed in X. We study the properties of C-closed spaces. Among other results, it is shown that countably compact C-closed spaces have countable tightness and under Martin's Axiom or 2ω0<2ω1, C-closed is equivalent to sequential for compact Hausdorff spaces. Furthermore, every hereditarily quasi-k Hausdorff space is Fréchet-Urysohn, which generalizes a theorem of Arhangel'sk
in 4]. Also every hereditarily q-space is hereditarily of pointwise countable type and contains an open dense first countable subspace. |
| |
Keywords: | C-closed countably compact quasi-k space tightness sequential q-spaces spaces of point-countable type Hereditary properties |
本文献已被 ScienceDirect 等数据库收录! |
|