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Čech-completeness and ultracompleteness in “nice spaces”

Miguel López de Luna; Vladimir Vladimirovich Tkachuk — 2002

Commentationes Mathematicae Universitatis Carolinae

We prove that if $X^{n}$ is a union of $n$ subspaces of pointwise countable type then the space $X$ is of pointwise countable type. If $X^{ω}$ is a countable union of ultracomplete spaces, the space $X^{ω}$ is ultracomplete. We give, under CH, an example of a Čech-complete, countably compact and non-ultracomplete space, giving thus a partial answer to a question asked in [BY2].

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