Displaying similar documents to “Homeomorphisms of products of subsets of the Cantor discontinuum”

Point-countable π-bases in first countable and similar spaces

V. V. Tkachuk (2005)

Fundamenta Mathematicae

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It is a classical result of Shapirovsky that any compact space of countable tightness has a point-countable π-base. We look at general spaces with point-countable π-bases and prove, in particular, that, under the Continuum Hypothesis, any Lindelöf first countable space has a point-countable π-base. We also analyze when the function space C p ( X ) has a point-countable π -base, giving a criterion for this in terms of the topology of X when l*(X) = ω. Dealing with point-countable π-bases makes...

In search for Lindelöf C p ’s

Raushan Z. Buzyakova (2004)

Commentationes Mathematicae Universitatis Carolinae

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It is shown that if X is a first-countable countably compact subspace of ordinals then C p ( X ) is Lindelöf. This result is used to construct an example of a countably compact space X such that the extent of C p ( X ) is less than the Lindelöf number of C p ( X ) . This example answers negatively Reznichenko’s question whether Baturov’s theorem holds for countably compact spaces.

A remark on the tightness of products

Oleg Okunev (1996)

Commentationes Mathematicae Universitatis Carolinae

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We observe the existence of a σ -compact, separable topological group G and a countable topological group H such that the tightness of G is countable, but the tightness of G × H is equal to 𝔠 .

A universal property of C 0 -semigroups

Gerd Herzog, Christoph Schmoeger (2009)

Commentationes Mathematicae Universitatis Carolinae

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Let T : [ 0 , ∞ ) → L ( E ) be a C 0 -semigroup with unbounded generator A : D ( A ) → E . We prove that ( T ( t ) x - x ) / t has generically a very irregular behaviour for x ∉ D ( A ) as t → 0 + .