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A Corson compact L-space from a Suslin tree

Peter Nyikos (2015)

Colloquium Mathematicae

The completion of a Suslin tree is shown to be a consistent example of a Corson compact L-space when endowed with the coarse wedge topology. The example has the further properties of being zero-dimensional and monotonically normal.

Bourbaki's Fixpoint Lemma reconsidered

Bernhard Banaschewski (1992)

Commentationes Mathematicae Universitatis Carolinae

A constructively valid counterpart to Bourbaki’s Fixpoint Lemma for chain-complete partially ordered sets is presented to obtain a condition for one closure system in a complete lattice L to be stable under another closure operator of L . This is then used to deal with coproducts and other aspects of frames.

Countable compactness and p -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

For ∅ ≠ M ⊆ ω * , we say that X is quasi M -compact, if for every f : ω → X there is p ∈ M such that f ¯ ( p ) ∈ X , where f ¯ is the Stone-Čech extension of f . In this context, a space X is countably compact iff X is quasi ω * -compact. If X is quasi M -compact and M is either finite or countable discrete in ω * , then all powers of X are countably compact. Assuming C H , we give an example of a countable subset M ⊆ ω * and a quasi M -compact space X whose square is not countably compact, and show that in a model of A. Blass and S. Shelah every quasi...

MAD families and P -points

Salvador García-Ferreira, Paul J. Szeptycki (2007)

Commentationes Mathematicae Universitatis Carolinae

The Katětov ordering of two maximal almost disjoint (MAD) families 𝒜 and ℬ is defined as follows: We say that 𝒜 ≤ K ℬ if there is a function f : ω → ω such that f - 1 ( A ) ∈ ℐ ( ℬ ) for every A ∈ ℐ ( 𝒜 ) . In [Garcia-Ferreira S., Hrušák M., Ordering MAD families a la Katětov, J. Symbolic Logic 68 (2003), 1337–1353] a MAD family is called K -uniform if for every X ∈ ℐ ( 𝒜 ) + , we have that 𝒜 | X ≤ K 𝒜 . We prove that CH implies that for every K -uniform MAD family 𝒜 there is a P -point p of ω * such that the set of all Rudin-Keisler predecessors of p is dense in the...

More reflections on compactness

Lúcia R. Junqueira, Franklin D. Tall (2003)

Fundamenta Mathematicae

We consider the question of when X M = X , where X M is the elementary submodel topology on X ∩ M, especially in the case when X M is compact.

On subsets of Alexandroff duplicates

Takemi Mizokami (2005)

Commentationes Mathematicae Universitatis Carolinae

We characterize the subsets of the Alexandroff duplicate which have a G δ -diagonal and the subsets which are M-spaces in the sense of Morita.

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