We obtain an independence result connected to the classic Moore–Mrowka problem. A property known to be intermediate between sequential and countable tightness in the class of compact spaces is the… Click to show full abstract
We obtain an independence result connected to the classic Moore–Mrowka problem. A property known to be intermediate between sequential and countable tightness in the class of compact spaces is the notion of a space being C-closed. A space is C-closed if every countably compact subset is closed. We prove it is consistent to have a compact C-closed space that is not sequential. Our example also answers a question of Arhangelskii by producing a compactification of the countable discrete space which is not itself sequential and yet it has a Fréchet–Urysohn remainder. Ismail and Nyikos showed that compact C-closed spaces are sequential if $${2^{\mathfrak{t}} > 2^\omega}$$2t>2ω. We prove that compact C-closed spaces are sequential also holds in the standard Cohen model.
               
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