Geodesic
Čech-completeness and ultracompleteness in “nice spaces”
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 515-524.

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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].
Classification : 54C10, 54C25, 54D06, 54D25, 54D35, 54D70, 54E50, 54F65, 54H11
Keywords: ultracompleteness; Čech-completeness; countable type; pointwise countable type 
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de Luna, Miguel López; Tkachuk, Vladimir V. Čech-completeness and ultracompleteness in “nice spaces”. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) no. 3, pp. 515-524. http://geodesic.mathdoc.fr/item/CMUC_2002__43_3_a11/