The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “Hereditarily Hurewicz spaces and Arhangel'skii sheaf amalgamations”

Some generalizations of Olivier's theorem

Alain Faisant, Georges Grekos, Ladislav Mišík (2016)

Mathematica Bohemica

Similarity:

Let n = 1 a n be a convergent series of positive real numbers. L. Olivier proved that if the sequence ( a n ) is non-increasing, then lim n n a n = 0 . In the present paper: (a) We formulate and prove a necessary and sufficient condition for having lim n n a n = 0 ; Olivier’s theorem is a consequence of our Theorem . (b) We prove properties analogous to Olivier’s property when the usual convergence is replaced by the -convergence, that is a convergence according to an ideal of subsets of . Again, Olivier’s theorem is a consequence...

Diagonals of separately continuous functions of n variables with values in strongly σ -metrizable spaces

Olena Karlova, Volodymyr Mykhaylyuk, Oleksandr Sobchuk (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove the result on Baire classification of mappings f : X × Y Z which are continuous with respect to the first variable and belongs to a Baire class with respect to the second one, where X is a P P -space, Y is a topological space and Z is a strongly σ -metrizable space with additional properties. We show that for any topological space X , special equiconnected space Z and a mapping g : X Z of the ( n - 1 ) -th Baire class there exists a strongly separately continuous mapping f : X n Z with the diagonal g . For wide classes...

Baire one functions and their sets of discontinuity

Jonald P. Fenecios, Emmanuel A. Cabral, Abraham P. Racca (2016)

Mathematica Bohemica

Similarity:

A characterization of functions in the first Baire class in terms of their sets of discontinuity is given. More precisely, a function f : is of the first Baire class if and only if for each ϵ > 0 there is a sequence of closed sets { C n } n = 1 such that D f = n = 1 C n and ω f ( C n ) < ϵ for each n where ω f ( C n ) = sup { | f ( x ) - f ( y ) | : x , y C n } and D f denotes the set of points of discontinuity of f . The proof of the main theorem is based on a recent ϵ - δ characterization of Baire class one functions as well as on a well-known theorem due to Lebesgue. Some direct applications...

On strong measure zero subsets of κ 2

Aapo Halko, Saharon Shelah (2001)

Fundamenta Mathematicae

Similarity:

We study the generalized Cantor space κ 2 and the generalized Baire space κ κ as analogues of the classical Cantor and Baire spaces. We equip κ κ with the topology where a basic neighborhood of a point η is the set ν: (∀j < i)(ν(j) = η(j)), where i < κ. We define the concept of a strong measure zero set of κ 2 . We prove for successor κ = κ < κ that the ideal of strong measure zero sets of κ 2 is κ -additive, where κ is the size of the smallest unbounded family in κ κ , and that the generalized Borel...

Baire classes of complex L 1 -preduals

Pavel Ludvík, Jiří Spurný (2015)

Czechoslovak Mathematical Journal

Similarity:

Let X be a complex L 1 -predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire- α functions on the set ext B X * of the extreme points of the dual unit ball B X * to the whole unit ball B X * . As a corollary we show that, given α [ 1 , ω 1 ) , the intrinsic α -th Baire class of X can be identified with the space of bounded homogeneous Baire- α functions on the set ext B X * when ext B X * satisfies certain topological assumptions. The paper is intended to be a complex counterpart to...

A remark on functions continuous on all lines

Luděk Zajíček (2019)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We prove that each linearly continuous function f on n (i.e., each function continuous on all lines) belongs to the first Baire class, which answers a problem formulated by K. C. Ciesielski and D. Miller (2016). The same result holds also for f on an arbitrary Banach space X , if f has moreover the Baire property. We also prove (extending a known finite-dimensional result) that such f on a separable X is continuous at all points outside a first category set which is also null in any usual...

A note on the multiplier ideals of monomial ideals

Cheng Gong, Zhongming Tang (2015)

Czechoslovak Mathematical Journal

Similarity:

Let 𝔞 [ x 1 , ... , x n ] be a monomial ideal and 𝒥 ( 𝔞 c ) the multiplier ideal of 𝔞 with coefficient c . Then 𝒥 ( 𝔞 c ) is also a monomial ideal of [ x 1 , ... , x n ] , and the equality 𝒥 ( 𝔞 c ) = 𝔞 implies that 0 < c < n + 1 . We mainly discuss the problem when 𝒥 ( 𝔞 ) = 𝔞 or 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 for all 0 < ε < 1 . It is proved that if 𝒥 ( 𝔞 ) = 𝔞 then 𝔞 is principal, and if 𝒥 ( 𝔞 n + 1 - ε ) = 𝔞 holds for all 0 < ε < 1 then 𝔞 = ( x 1 , ... , x n ) . One global result is also obtained. Let 𝔞 ˜ be the ideal sheaf on n - 1 associated with 𝔞 . Then it is proved that the equality 𝒥 ( 𝔞 ˜ ) = 𝔞 ˜ implies that 𝔞 ˜ is principal.

Coloring Cantor sets and resolvability of pseudocompact spaces

István Juhász, Lajos Soukup, Zoltán Szentmiklóssy (2018)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let us denote by Φ ( λ , μ ) the statement that 𝔹 ( λ ) = D ( λ ) ω , i.e. the Baire space of weight λ , has a coloring with μ colors such that every homeomorphic copy of the Cantor set in 𝔹 ( λ ) picks up all the μ colors. We call a space X π -regular if it is Hausdorff and for every nonempty open set U in X there is a nonempty open set V such that V ¯ U . We recall that a space X is called feebly compact if every locally finite collection of open sets in X is finite. A Tychonov space is pseudocompact if and...