Metrizable DH-spaces of the first category

Medvedev, S. V.

doi:10.1016/j.topol.2014.08.025

Cited by 7 publications

(5 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Knaster-Reichbach covers were introduced in [30] and have been successfully applied by several authors, including van Engelen, Medvedev and Ostrovskiȋ. Let us mention for example the articles [5], [22], [23], [24], [25] and [34], where one can find much more general results than the ones stated here. The first application of this technique to the theory of countable dense homogeneity was recently given by Hernández-Gutiérrez, Hrušák and van Mill in [10].…”

Section: Knaster-reichbach Coversmentioning

confidence: 55%

See 1 more Smart Citation

Countable Dense Homogeneity in Powers of Zero-dimensional Definable Spaces

Medini¹

2015

Can. math. bull.

View full text Add to dashboard Cite

Abstract. We show that, for a coanalytic subspace X of 2 ω , the countable dense homogeneity of X ω is equivalent to X being Polish. This strengthens a result of Hrušák and Zamora Avilés. Then, inspired by results of Hernández-Gutiérrez, Hrušák and van Mill, using a technique of Medvedev, we construct a non-Polish subspace X of 2 ω such that X ω is countable dense homogeneous. This gives the first ZFC answer to a question of Hrušák and Zamora Avilés. Furthermore, since our example is consistently analytic, the equivalence result mentioned above is sharp. Our results also answer a question of Medini and Milovich. Finally, we show that if every countable subset of a zero-dimensional separable metrizable space X is included in a Polish subspace of X then X ω is countable dense homogeneous.

show abstract

Section: Knaster-reichbach Coversmentioning

confidence: 55%

“…The technique used in the proof of the following theorem is essentially due to Medvedev (see [25,Theorem 5]). Theorem 7.3.…”

Section: The Main Resultsmentioning

confidence: 99%

Countable Dense Homogeneity in Powers of Zero-dimensional Definable Spaces

Medini¹

2015

Can. math. bull.

View full text Add to dashboard Cite

show abstract

“…Let us note that, for metrizable spaces, the assertion of Theorem 3.1 is known (see [Me,Corollary 3] or cf. remarks preceding Proposition 2.2 in [HG2]).…”

Section: All Cdh Topological Vector Spaces Are Baire Spacesmentioning

confidence: 99%

A countable dense homogeneous topological vector space is a Baire space

Dobrowolski¹,

Krupski²,

Marciszewski³

2020

Preprint

View full text Add to dashboard Cite

We prove that every homogeneous countable dense homogeneous topological space containing a copy of the Cantor set is a Baire space. In particular, every countable dense homogeneous topological vector space is a Baire space. It follows that, for any nondiscrete metrizable space X, the function space Cp(X) is not countable dense homogeneous. This answers a question posed recently by R. Hernández-Gutiérrez. We also conclude that, for any infinite dimensional Banach space E (dual Banach space E * ), the space E equipped with the weak topology (E * with the weak * topology) is not countable dense homogeneous. We generalize some results of Hrušák, Zamora Avilés, and Hernández-Gutiérrez concerning countable dense homogeneous products.

show abstract

“…A topological space true(X,ℑtrue) is homogeneous if for all x,y∈X, there is a homeomorphism f:(X,ℑ)false⟶(X,ℑ) such that ffalse(xfalse)goodbreakafter=y. Since homogeneity concepts are of importance in general topology and still a hot area of research, as appears in [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], we see that it is suitable to extend the homogeneity concept to include soft topological spaces. One of our main goals of the present work is to show how the definition of homogeneity in ordinary topological spaces can be modified in order to define its extension in soft topological spaces.…”

Section: Introductionmentioning

confidence: 99%

On some generated soft topological spaces and soft homogeneity

Ghour

Bin-Saadon

2019

Heliyon

View full text Add to dashboard Cite

We introduce soft homogeneity as an extension of homogeneity in ordinary topological spaces. Based on the generated soft topology of a given indexed family of classical topologies inspite of a one topology given by Terepeta in [16] , we investigate soft minimal open set and homogeneity relation between the generated soft topology and the given indexed family of topologies. We introduce several results, examples and counterexamples.

show abstract

Metrizable DH-spaces of the first category

Cited by 7 publications

References 14 publications

Countable Dense Homogeneity in Powers of Zero-dimensional Definable Spaces

Countable Dense Homogeneity in Powers of Zero-dimensional Definable Spaces

A countable dense homogeneous topological vector space is a Baire space

On some generated soft topological spaces and soft homogeneity

Contact Info

Product

Resources

About