Čech-completeness and ultracompleteness in “nice” spaces

  • Miguel López de Luna, Vladimir V. Tkachuk
  • Published 2002


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