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ultracompleteness; Čech-completeness; countable type; pointwise countable type
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^\omega $ is a countable union of ultracomplete spaces, the space $X^\omega $ 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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