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A topology is never an ultrafilter, as the empty set is open. Note that the definition allows for a given set and its complement to be both open. Having said that, I have serious doubts about the notability of this
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Door spaces and their generalization were studied in a paper by WH and AM published in the
Bulletin of Polish Academy of Science, around y.1964.
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I found out about door spaces five minutes ago. Is it correct to say that a door space topology on X is an
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