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Bad Wadge-like reducibilities on the Baire space

Luca Motto Ros (2014)

Fundamenta Mathematicae

We consider various collections of functions from the Baire space ω ω into itself naturally arising in (effective) descriptive set theory and general topology, including computable (equivalently, recursive) functions, contraction mappings, and functions which are nonexpansive or Lipschitz with respect to suitable complete ultrametrics on ω ω (compatible with its standard topology). We analyze the degree-structures induced by such sets of functions when used as reducibility notions between subsets of...

Balcar's theorem on supports

Lev Bukovský (2018)

Commentationes Mathematicae Universitatis Carolinae

In A theorem on supports in the theory of semisets [Comment. Math. Univ. Carolinae 14 (1973), no. 1, 1–6] B. Balcar showed that if σ ⊆ D ∈ M is a support, M being an inner model of ZFC, and 𝒫 ( D ∖ σ ) ∩ M = r ` ` σ with r ∈ M , then r determines a preorder " ⪯ " of D such that σ becomes a filter on ( D , ⪯ ) generic over M . We show that if the relation r is replaced by a function 𝒫 ( D ∖ σ ) ∩ M = f - 1 ( σ ) , then there exists an equivalence relation " ∼ " on D and a partial order on D / ∼ such that D / ∼ is a complete Boolean algebra, σ / ∼ is a generic filter and [ f ( u ) ] ∼ = - ∑ ( u / ∼ ) for any u ⊆ D , u ∈ M .

Banach spaces without minimal subspaces – Examples

Valentin Ferenczi, Christian Rosendal (2012)

Annales de l’institut Fourier

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11],by classifying them according to which side of the dichotomies they fall.

Banach-Mazur game played in partially ordered sets

Wiesław Kubiś (2016)

Banach Center Publications

Concepts, definitions, notions, and some facts concerning the Banach-Mazur game are customized to a more general setting of partial orderings. It is applied in the theory of Fraïssé limits and beyond, obtaining simple proofs of universality of certain objects and classes.

Banach’s Continuous Inverse Theorem and Closed Graph Theorem

Hideki Sakurai, Hiroyuki Okazaki, Yasunari Shidama (2012)

Formalized Mathematics

In this article we formalize one of the most important theorems of linear operator theory - the Closed Graph Theorem commonly used in a standard text book such as [10] in Chapter 24.3. It states that a surjective closed linear operator between Banach spaces is bounded.

Base-base paracompactness and subsets of the Sorgenfrey line

Strashimir G. Popvassilev (2012)

Mathematica Bohemica

A topological space X is called base-base paracompact (John E. Porter) if it has an open base ℬ such that every base ℬ ' ⊆ ℬ has a locally finite subcover 𝒞 ⊆ 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.

Basic pseudorings

Ivan Chajda, Miroslav Kolařík (2009)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.

Bell-type inequalities for parametric families of triangular norms

Saskia Janssens, Bernard De Baets, Hans De Meyer (2004)

Kybernetika

In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities;...

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