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Displaying similar documents to “A note on splittable spaces”

Countable compactness and p -limits

Salvador García-Ferreira, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

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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...

Topologies on groups determined by right cancellable ultrafilters

Igor V. Protasov (2009)

Commentationes Mathematicae Universitatis Carolinae

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For every discrete group G , the Stone-Čech compactification β G of G has a natural structure of a compact right topological semigroup. An ultrafilter p G * , where G * = β G G , is called right cancellable if, given any q , r G * , q p = r p implies q = r . For every right cancellable ultrafilter p G * , we denote by G ( p ) the group G endowed with the strongest left invariant topology in which p converges to the identity of G . For any countable group G and any right cancellable ultrafilters p , q G * , we show that G ( p ) is homeomorphic to G ( q ) if...

MAD families and P -points

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

Commentationes Mathematicae Universitatis Carolinae

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The Katětov ordering of two maximal almost disjoint (MAD) families 𝒜 and is defined as follows: We say that 𝒜 K if there is a function f : ω ω such that f - 1 ( A ) ( ) for every A ( 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 ( 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...