Modifications of sequence selection principles

Bukovský, Lev; Šupina, Jaroslav

doi:10.1016/j.topol.2013.07.030

Cited by 4 publications

(16 citation statements)

References 18 publications

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“…Proposition 4.3 says that DL(F, C(X)) is also related to such decompositions. The equivalence of (1) and (2) is well-known due to [14] or [2], the equivalence of (1) and 10 They say that function is piece-wise continuous, i.e., it satisfies condition (3) of our Proposition 4.3 with increasing sequence F n ; n ∈ ω . For ongoing research see e.g.…”

Section: Jayne-rogers Propertymentioning

confidence: 99%

“…For a family F ⊆ X R, L. Bukovský and the author say in [10] that X is a wQN F -space if each sequence of functions from F converging to zero on X contains a subsequence that converges quasi-normally. A wQNspace is a wQN C(X) -space and if each sequence of continuous functions converging to zero on X converges quasi-normally, then X is called a QN-space (see [7]).…”

Section: Preliminaries and Basic Notionsmentioning

confidence: 99%

“…Rogers [20] proved that every Δ 0 2 -measurable function on an analytic subset of a Polish space is a discrete limit of a sequence of continuous functions. 10 We shall investigate a generalization of the last property. Let F, G ⊆ X R. We say that a topological space X has a property DL(F , G) if any function from F is a discrete limit of a sequence of functions from G. Main result of this section which will be proved later in the section reads as follows (a) Let X be a topological space.…”

Section: Jayne-rogers Propertymentioning

confidence: 99%

See 2 more Smart Citations

On Ohta–Sakai's properties of a topological space

Šupina

2015

Topology and its Applications

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We investigate modifications of properties USC s and LSC s introduced by H. Ohta and M. Sakai [30]. Our property wED(U , C(X)) holds in any S 1 (Γ, Γ)-space and property wED(L, C(X)) holds in perfectly normal QN-space. We present their covering characterizations and hereditary properties. Our main result is that a topological space X is an S 1 (Γ, Γ)-space if and only if X is both, a wQN-space and possesses wED(U , C(X)). Property wED(L, C(X)) is related to the condition "to be a discrete limit of a sequence of continuous functions" which is briefly studied in the paper as well. Moreover, for perfectly normal space we show that original property USCs is hereditary for Δ 0 2 subsets.

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Section: Jayne-rogers Propertymentioning

confidence: 99%

Section: Preliminaries and Basic Notionsmentioning

confidence: 99%

Section: Jayne-rogers Propertymentioning

confidence: 99%

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On Ohta–Sakai's properties of a topological space

Šupina

2015

Topology and its Applications

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“…By their main result, and by L. B u k o vs ký, I. R e c l a w and M. R e p i c ký [3], we have that a perfectly normal topological space X is a QN-space if and only if X has Hurewicz property hereditarily and every Δ 0 2 -measurable function on X is a discrete limit of continuous functions. The latter property is called Jayne-Rogers property in [4], since J. E. J a y n e and C. A. R o g e r s [9] showed that any analytic subset of a Polish space has Jayne-Rogers property. However, it seems that the question which topological spaces possess Jayne-Rogers property is an open problem.…”

Section: Jaroslavšupina -Dávid Uhrikmentioning

confidence: 99%

“…Basic properties are summarized in the following assertion which, for arbitrary topological space, is proved in a monograph by R. S i k o r s k i [15], mostly in Theorem V.10.1. 4 In what follows for clarity, we do not denote the topological space.…”

Section: Hierarchiesmentioning

confidence: 99%

On a Lindenbaum Composition Theorem

Šupina

Uhrik

2019

Tatra Mountains Mathematical Publications

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We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les superpositions des fonctions représentables analytiquement, Fund. Math. 23 (1934), 15–37] proved for the real line hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper Δ02-measurable functions.

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On sequence selection properties

Šupina¹

2013

Filomat

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We investigate modifications of the selection principles for various kinds of convergences introduced by L. Bukovský and J.Šupina [9]. We show that if we restrict our selection principles to continuous functions then they split just to two equivalence classes. Considering other families of limit functions we obtain our main result saying that selecting "from every sequence of a sequence of sequences of functions" or just "from infinitely many sequences" can produce properties which can be consistently distinguished. Moreover, we show that our selection principles are characterizations of some properties of a topological space, e.g. hereditarily Hurewicz space or hereditarily S 1 (Γ, Γ)-space.

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Modifications of sequence selection principles

Cited by 4 publications

References 18 publications

On Ohta–Sakai's properties of a topological space

On Ohta–Sakai's properties of a topological space

On a Lindenbaum Composition Theorem

On sequence selection properties

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