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A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $ℬ$ such that every base $ℬ^{'} \subseteq ℬ$ has a locally finite subcover $𝒞 \subseteq ℬ^{'}$ . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

Bernstein sets with algebraic properties

Marcin Kysiak (2009)

Open Mathematics

We construct Bernstein sets in ℝ having some additional algebraic properties. In particular, solving a problem of Kraszewski, Rałowski, Szczepaniak and Żeberski, we construct a Bernstein set which is a < c-covering and improve some other results of Rałowski, Szczepaniak and Żeberski on nonmeasurable sets.

Besicovitch via Baire

T. W. Körner (2003)

Studia Mathematica

We construct various Besicovitch sets using Baire category arguments.

Besicovitch's circle pairs, analytic capacity, and Cauchy integrals for a class of unrectifiable 1-sets.

Farag, Hany M. (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

Best simultaneous $L_{p}$ approximations

Yusuf Karakuş (1998)

Czechoslovak Mathematical Journal

In this paper we study simultaneous approximation of $n$ real-valued functions in $L_{p} [a, b]$ and give a generalization of some related results.

Beyond Lebesgue and Baire II: Bitopology and measure-category duality

N. H. Bingham, A. J. Ostaszewski (2010)

Colloquium Mathematicae

We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions...

Big set of measure zero

Ladislav Mišík (2001)

Acta Mathematica et Informatica Universitatis Ostraviensis

Bimeasurable maps

John Michaels (1970)

Fundamenta Mathematicae

Borel and monotone hierarchies and extension of Rényi probability spaces

B. Aniszczyk, J. Burzyk, A. Kamiński (1987)

Colloquium Mathematicae

Borel and weakly Borel sets in Banach spaces

Preiss, D. (1977)

Abstracta. 5th Winter School on Abstract Analysis

Borel classes in AST. Measurability, cuts and equivalence

Martin Kalina, Pavol Zlatoš (1989)

Commentationes Mathematicae Universitatis Carolinae

Borel equivalence and isomorphism of coanalytic sets [Book]

Douglas Cenzer, R. Daniel Mauldin (1984)

Borel extensions of Baire measures in ZFC

Menachem Kojman, Henryk Michalewski (2011)

Fundamenta Mathematicae

We prove: 1) Every Baire measure on the Kojman-Shelah Dowker space admits a Borel extension. 2) If the continuum is not real-valued-measurable then every Baire measure on M. E. Rudin's Dowker space admits a Borel extension. Consequently, Balogh's space remains the only candidate to be a ZFC counterexample to the measure extension problem of the three presently known ZFC Dowker spaces.

Borel partitions of unity and lower Carathéodory multifunctions

S. Srivastava (1995)

Fundamenta Mathematicae

We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A (ℰ \otimes ℬ (X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations...

Borel parts of the spectrum of an operator and of the operator algebra of a separable Hilbert space

Piotr Niemiec (2012)

Studia Mathematica

For a linear operator T in a Banach space let $σ_{p} (T)$ denote the point spectrum of T, let $σ_{p, n} (T)$ for finite n > 0 be the set of all $λ \in σ_{p} (T)$ such that dim ker(T - λ) = n and let $σ_{p, \infty} (T)$ be the set of all $λ \in σ_{p} (T)$ for which ker(T - λ) is infinite-dimensional. It is shown that $σ_{p} (T)$ is $ℱ_{σ}$ , $σ_{p, \infty} (T)$ is $ℱ_{σ δ}$ and for each finite n the set $σ_{p, n} (T)$ is the intersection of an $ℱ_{σ}$ set and a $_{δ}$ set provided T is closable and the domain of T is separable and weakly σ-compact. For closed densely defined operators in a separable Hilbert space a more detailed decomposition...

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