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Displaying 621 – 640 of 8504

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A quest for nice kernels of neighbourhood assignments

Raushan Z. Buzyakova, Vladimir Vladimirovich Tkachuk, Richard Gordon Wilson (2007)

Commentationes Mathematicae Universitatis Carolinae

Given a topological property (or a class) 𝒫 , the class 𝒫 * dual to 𝒫 (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment { O x : x X } there is Y X with Y 𝒫 and { O x : x Y } = X . The spaces from 𝒫 * are called dually 𝒫 . We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define D -spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space...

A Ramsey theorem for polyadic spaces

Murray Bell (1996)

Fundamenta Mathematicae

A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that ( α κ ) ω is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage....

A reconstruction theorem for locally moving groups acting on completely metrizable spaces

Edmund Ben-Ami (2010)

Fundamenta Mathematicae

Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category...

A relatively free topological group that is not varietal free

Vladimir Pestov, Dmitri Shakhmatov (1998)

Colloquium Mathematicae

Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.

A remark on a theorem of Solecki

Petr Holický, Luděk Zajíček, Miroslav Zelený (2005)

Commentationes Mathematicae Universitatis Carolinae

S. Solecki proved that if is a system of closed subsets of a complete separable metric space X , then each Suslin set S X which cannot be covered by countably many members of contains a G δ set which cannot be covered by countably many members of . We show that the assumption of separability of X cannot be removed from this theorem. On the other hand it can be removed under an extra assumption that the σ -ideal generated by is locally determined. Using Solecki’s arguments, our result can be used...

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