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On powers of Lindelöf spaces

Isaac Gorelic (1994)

Commentationes Mathematicae Universitatis Carolinae

We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space X whose square X 2 is again Lindelöf but its cube X 3 has a closed discrete subspace of size 𝔠 + , hence the Lindelöf degree L ( X 3 ) = 𝔠 + . In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space X such that L ( X n ) = 0 for all positive integers n , but L ( X 0 ) = 𝔠 + = 2 .

On preimages of ultrafilters in ZF

Horst Herrlich, Paul Howard, Kyriakos Keremedis (2016)

Commentationes Mathematicae Universitatis Carolinae

We show that given infinite sets X , Y and a function f : X Y which is onto and n -to-one for some n , the preimage of any ultrafilter of Y under f extends to an ultrafilter. We prove that the latter result is, in some sense, the best possible by constructing a permutation model with a set of atoms A and a finite-to-one onto function f : A ω such that for each free ultrafilter of ω its preimage under f does not extend to an ultrafilter. In addition, we show that in there exists an ultrafilter compact pseudometric...

On pre-Urysohn spaces.

Paul, Ramprasad, Bhattacharyya, P. (1999)

Bulletin of the Malaysian Mathematical Society. Second Series

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