On spaces in which countably compact sets are closed, and hereditary properties
- Ismail, Mohammad
- Nyikos, Peter
DOIAbstract
AbstractA 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'skĩĩ in [4]. Also every hereditarily q-space is hereditarily of pointwise countable type and contains an open dense first countable subspace
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