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Homogeneity and rigidity in Erdös spaces

Klaas P. Hart, Jan van Mill (2018)

Commentationes Mathematicae Universitatis Carolinae

The classical Erdös spaces are obtained as the subspaces of real separable Hilbert space consisting of the points with all coordinates rational or all coordinates irrational, respectively. One can create variations by specifying in which set each coordinate is allowed to vary. We investigate the homogeneity of the resulting subspaces. Our two main results are: in case all coordinates are allowed to vary in the same set the subspace need not be homogeneous, and by specifying different sets for different...

Means on scattered compacta

T. Banakh, R. Bonnet, W. Kubis (2014)

Topological Algebra and its Applications

We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.

Metrization criteria for compact groups in terms of their dense subgroups

Dikran Dikranjan, Dmitri Shakhmatov (2013)

Fundamenta Mathematicae

According to Comfort, Raczkowski and Trigos-Arrieta, a dense subgroup D of a compact abelian group G determines G if the restriction homomorphism Ĝ → D̂ of the dual groups is a topological isomorphism. We introduce four conditions on D that are necessary for it to determine G and we resolve the following question: If one of these conditions holds for every dense (or G δ -dense) subgroup D of G, must G be metrizable? In particular, we prove (in ZFC) that a compact abelian group determined by all its...

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 the k -Baire property

Alessandro Fedeli (1993)

Commentationes Mathematicae Universitatis Carolinae

In this note we show the following theorem: “Let X be an almost k -discrete space, where k is a regular cardinal. Then X is k + -Baire iff it is a k -Baire space and every point- k open cover 𝒰 of X such that card ( 𝒰 ) ≤ k is locally- k at a dense set of points.” For k = ℵ 0 we obtain a well-known characterization of Baire spaces. The case k = ℵ 1 is also discussed.

On Weakly Measurable Functions

Szymon Żeberski (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".

Remarks on sequence-covering maps

Luong Quoc Tuyen (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that each sequence-covering and boundary-compact map on g -metrizable spaces is 1-sequence-covering. Then, we give some relationships between sequence-covering maps and 1-sequence-covering maps or weak-open maps, and give an affirmative answer to the problem posed by F.C. Lin and S. Lin in [Lin.F.C.and.Lin.S-2011].

Currently displaying 21 – 40 of 55