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Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the topology...

Around cofin

Andrzej Rosłanowski, Saharon Shelah (2014)

Colloquium Mathematicae

We show the consistency of "there is a nice σ-ideal ℐ on the reals with add(ℐ) = ℵ₁ which cannot be represented as the union of a strictly increasing sequence of length ω₁ of σ-subideals". This answers [Borodulin-Nadzieja and Głąb, Math. Logic Quart. 57 (2011), 582-590, Problem 6.2(ii)].

Around splitting and reaping

Jörg Brendle (1998)

Commentationes Mathematicae Universitatis Carolinae

We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number 𝔰 or its dual, the reaping number 𝔯 .

Associative n -dimensional copulas

Andrea Stupňanová, Anna Kolesárová (2011)

Kybernetika

The associativity of n -dimensional copulas in the sense of Post is studied. These copulas are shown to be just n -ary extensions of associative 2-dimensional copulas with special constraints, thus they solve an open problem of R. Mesiar posed during the International Conference FSTA 2010 in Liptovský Ján, Slovakia.

Asymmetric tie-points and almost clopen subsets of ℕ *

Alan S. Dow, Saharon Shelah (2018)

Commentationes Mathematicae Universitatis Carolinae

A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of ℕ * . One especially important application, due to Veličković, was to the existence of nontrivial involutions on ℕ * . A tie-point of ℕ * has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost clopen set...

Automata, Borel functions and real numbers in Pisot base

Benoit Cagnard, Pierre Simonnet (2007)

RAIRO - Theoretical Informatics and Applications

This note is about functions ƒ : Aω → Bω whose graph is recognized by a Büchi finite automaton on the product alphabet A x B. These functions are Baire class 2 in the Baire hierarchy of Borel functions and it is decidable whether such function are continuous or not. In 1920 W. Sierpinski showed that a function f : ℝ → ℝ is Baire class 1 if and only if both the overgraph and the undergraph of f are Fσ. We show that such characterization is also true for functions on infinite words if we replace the real...

Automorphisms of ( λ ) / ℐ κ

Paul Larson, Paul McKenney (2016)

Fundamenta Mathematicae

We study conditions on automorphisms of Boolean algebras of the form ( λ ) / ℐ κ (where λ is an uncountable cardinal and ℐ κ is the ideal of sets of cardinality less than κ ) which allow one to conclude that a given automorphism is trivial. We show (among other things) that every automorphism of ( 2 κ ) / ℐ κ ⁺ which is trivial on all sets of cardinality κ⁺ is trivial, and that M A ℵ ₁ implies both that every automorphism of (ℝ)/Fin is trivial on a cocountable set and that every automorphism of (ℝ)/Ctble is trivial.

Axial permutations of ω²

Paweł Klinga (2016)

Colloquium Mathematicae

We prove that every permutation of ω² is a composition of a finite number of axial permutations, where each axial permutation moves only a finite number of elements on each axis.

Axioms which imply GCH

Jan Mycielski (2003)

Fundamenta Mathematicae

We propose some new set-theoretic axioms which imply the generalized continuum hypothesis, and we discuss some of their consequences.

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