On sequential separability of functional spaces

Osipov, Alexander V.; Pytkeev, E. G.

doi:10.1016/j.topol.2017.02.059

Cited by 8 publications

(8 citation statements)

References 4 publications

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“…Let ϕ be a identity map from X onto Y . By Theorem 3.1 in [4], ϕ is a bijection such that ϕ(D) is a Z σ -set of Y for any zero-set D of X. Since S ⊂ C(X), ϕ is a condensation.…”

Section: Resultsmentioning

confidence: 98%

On some properties of the space of upper semicontinuous functions

Osipov

Pytkeev

2019

Acta Math. Hungar.

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For a Tychonoff space X, we will denote by USC p (X) (B 1 (X)) the set of all real-valued upper semicontinuous functions (the set of all Baire functions of class 1) defined on X endowed with the pointwise convergence topology.In this paper we describe a class of Tychonoff spaces X for which the space USC p (X) is sequentially separable. Unexpectedly, it turns out that this class coincides with the class of spaces for which a stronger form of the sequential separability for the space B 1 (X) holds.

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“…Let ϕ be a identity map from X onto Y . By Theorem 3.1 in [4], ϕ is a bijection such that ϕ(D) is a Z σ -set of Y for any zero-set D of X. Since S ⊂ C(X), ϕ is a condensation.…”

Section: Resultsmentioning

confidence: 98%

On some properties of the space of upper semicontinuous functions

Osipov

Pytkeev

2019

Acta Math. Hungar.

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“…In [27], Osipov and Pytkeev have established criterion for B 1 (X) to be sequentially separable. Theorem 4.3.…”

Section: Continuous Functionsmentioning

confidence: 99%

“…In [27], Osipov and Pytkeev have established criterion for B 1 (X) to be strongly sequentially separable. For a Tychonoff space X and 0 < α ≤ ω 1 , the following statements are equivalent:…”

Section: Continuous Functionsmentioning

confidence: 99%

Application of selection principles in the study of the properties of function spaces

Osipov

2018

Acta Math. Hungar.

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For a Tychonoff space X, we denote by C p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence.In this paper we prove that:• if every finite power of X is Lindelëof then C p (X) to be strongly sequentially separable iff X is γ-set.• B α (X) -functions Baire class α (1 < α ≤ ω 1 ) on a Tychonoff space X with the pointwise topology -to be sequentially separable iff there exists a Baire isomorphism class α from a space X onto a σ-set.• B α (X) is strongly sequentially separable iff iw(X) = ℵ 0 and X is a Z α -cover γ-set for 0 < α ≤ ω 1 .• there is a consistent example of a set of reals X, such that C p (X) is strongly sequentially separable, but B 1 (X) is not strongly sequentially separable.• B(X) is sequentially separable, but is not strongly sequentially separable for a b-Sierpiński set X.

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“…In papers [1,2,3,4,5,8,9,12,13,14,16,17,18,19,20,21,24] (and many others) were investigated the applications of selection principles in the study of the properties of function spaces. In particular, the properties of the space C p (X) were investigated.…”

Section: Introductionmentioning

confidence: 99%