Direct and Inverse Problems of Baire Classification of Integrals Depending on a Parameter

Банах, Тарас; Kutsak, S. M.; Maslyuchenko, V. K.; Maslyuchenko, O. V.

doi:10.1007/s11253-005-0147-1

Cited by 5 publications

(8 citation statements)

References 1 publication

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“…In the case when X is a metrically quarter-stratifiable strongly countably-dimensional paracompact space or X is a metrically quarter-stratifiable space and Z is a locally convex equiconnected space (see definitions in [2]), the inclusion CC(X × X, Z) ⊆ B 1 (X 2 , Z) follows from [2, Corollary 5.2]. (4). Notice that an equiconnected space Z is locally arcwise connected.…”

Section: A Methods Of Constructing Of Separately Continuous Mappingsmentioning

confidence: 99%

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Diagonals of separately continuous functions and their analogs

Karlova¹,

Mykhaylyuk²,

Sobchuk³

2013

Topology and its Applications

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We prove that for a topological space X, an equiconnected space Z and a Baire-one mapping g : X → Z there exists a separately continuous mapping f :for every x ∈ X. Under a mild assumptions on X and Z we obtain that diagonals of separately continuous mappings f : X 2 → Z are exactly Baire-one functions, and diagonals of mappings f : X 2 → Z which are continuous on the first variable and Lipschitz (differentiable) on the second one, are exactly the functions of stable first Baire class.

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Section: A Methods Of Constructing Of Separately Continuous Mappingsmentioning

confidence: 99%

“…Let X and Y be topological spaces. A mapping f : X → Y is said to be σ-continuous (see [4]), if there exists a sequence (A n ) ∞ n=1 of closed sets A n ⊆ X such that all the restrictions f | An are continuous. In [3] such functions are called piecewise continuous.…”

Section: A Methods Of Constructing Of Separately Continuous Mappingsmentioning

confidence: 99%

Diagonals of separately continuous functions and their analogs

Karlova¹,

Mykhaylyuk²,

Sobchuk³

2013

Topology and its Applications

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“…Then the map g : X → Y is continuous and g| Cn = f | Cn . Hence, condition (2) holds. Now we suppose that under conditions (a) or (b) the implication (3)⇒(1) is valid for all ordinals γ ∈ [1, α) for some α ∈ (1, ω 1 ) and prove it for α.…”

Section: Stable Baire Classes and Their Characterizationmentioning

confidence: 94%

On stable Baire classes

Karlova

Mykhaylyuk

2016

Acta Math. Hungar.

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We introduce and study adhesive spaces. Using this concept we obtain a characterization of stable Baire maps f : X → Y of the class α for wide classes of topological spaces. In particular, we prove that for a topological space X and a contractible space Y a map f : X → Y belongs to the n'th stable Baire class if and only if there exist a sequence (f k ) ∞ k=1 of continuous maps f k : X → Y and a sequence (F k ) ∞ k=1 of functionally ambiguous sets of the n'th class in X such that f | F k = f k | F k for every k. Moreover, we show that every monotone function f : R → R is of the α'th stable Baire class if and only if it belongs to the first stable Baire class.1991 Mathematics Subject Classification. Primary 54C08, 54H05; Secondary 26A21.

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“…Then Lemma 2.2 yields a non-empty countable set D ⊂ X such that the restriction f |D has no continuity points. Applying Lemma 2.5 (3) to the restriction f |D, we can find a countable first-countable subset Q ⊂ D without finite open sets such that f |Q is bijective and f (Q) is a discrete subspace of Y . It is clear that f |Q has no continuity point.…”

Section: Proof Of Theorem 12mentioning

confidence: 99%

Weakly discontinuous and resolvable functions between topological spaces

Банах¹,

Bokalo²

2017

HJMS

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Abstract. We prove that a function f : X → Y from a first-countable (more generally, Preiss-Simon) space X to a regular space Y is weakly discontinuous (which means that every subspace A ⊂ X contains an open dense subset U ⊂ A such that f |U is continuous) if and only if f is open-resolvable (in the sense that for every open subset U ⊂ Y the preimage f −1 (U ) is a resolvable subset of X) if and only if f is resolvable (in the sense that for every resolvable subset R ⊂ Y the preimage f −1 (R) is a resolvable subset of X). For functions on metrizable spaces this characterization was announced (without proof) by Vinokurov in 1985.

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Direct and Inverse Problems of Baire Classification of Integrals Depending on a Parameter

Cited by 5 publications

References 1 publication

Diagonals of separately continuous functions and their analogs

Diagonals of separately continuous functions and their analogs

On stable Baire classes

Weakly discontinuous and resolvable functions between topological spaces

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