Displaying similar documents to “Further characterizations of boundedly UC spaces”

Ramsey, Lebesgue, and Marczewski sets and the Baire property

Patrick Reardon (1996)

Fundamenta Mathematicae

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We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented.  THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets.  THEOREM. In the Ellentuck topology on [ ω ] ω , ( s ) 0 is a proper subset of the hereditary ideal associated with (s).  We construct an example in the Ellentuck topology of a...

If it looks and smells like the reals...

Franklin Tall (2000)

Fundamenta Mathematicae

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Given a topological space ⟨X,T⟩ ∈ M, an elementary submodel of set theory, we define X M to be X ∩ M with topology generated by U ∩ M:U ∈ T ∩ M. We prove that if X M is homeomorphic to ℝ, then X = X M . The same holds for arbitrary locally compact uncountable separable metric spaces, but is independent of ZFC if “local compactness” is omitted.

Relatively compact spaces and separation properties

Aleksander V. Arhangel'skii, Ivan V. Yashchenko (1996)

Commentationes Mathematicae Universitatis Carolinae

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We consider the property of relative compactness of subspaces of Hausdorff spaces. Several examples of relatively compact spaces are given. We prove that the property of being a relatively compact subspace of a Hausdorff spaces is strictly stronger than being a regular space and strictly weaker than being a Tychonoff space.

The Dugundji extension property can fail in ωµ -metrizable spaces

Ian Stares, Jerry Vaughan (1996)

Fundamenta Mathematicae

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We show that there exist ω μ -metrizable spaces which do not have the Dugundji extension property ( 2 ω 1 with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

The sequential topology on complete Boolean algebras

Wiesław Główczyński, Bohuslav Balcar, Thomas Jech (1998)

Fundamenta Mathematicae

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We investigate the sequential topology τ s on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the space ( B , τ s ) is Hausdorff. We also characterize sequential cardinals.