Results 1 to 10 of about 48 (46)
Forum of Mathematics, PiWe introduce new types of examples of bounded degree acyclic Borel graphs and study their combinatorial properties in the context of descriptive combinatorics, using a generalization of the determinacy method of Marks [Mar16].
Sebastian Brandt +2 more
exaly +3 more sources
Brooks’ Theorem for Measurable Colorings
Forum of Mathematics, Sigma, 2016 We generalize Brooks’ theorem to show that if $G$ is a Borel graph on a standard Borel space $
Andrew Scott Marks +2 more
exaly +3 more sources
Uniformly factoring weakly compact operators and parametrised dualisation
Forum of Mathematics, Sigma, 2021 This article deals with the problem of when, given a collection $\mathcal {C}$ of weakly compact operators between separable Banach spaces, there exists a separable reflexive Banach space Z with a Schauder basis so that every element in $\mathcal {C ...
L. Antunes, K. Beanland, B. M. Braga
doaj +1 more source
Unicorn paths and hyperfiniteness for the mapping class group
Forum of Mathematics, Sigma, 2021 Let S be an orientable surface of finite type. Using Pho-on’s infinite unicorn paths, we prove the hyperfiniteness of orbit equivalence relations induced by the actions of the mapping class group of S on the Gromov boundaries of the arc graph and the ...
Piotr Przytycki, Marcin Sabok
doaj +1 more source
Haar null and Haar meager sets: a survey and new results
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020 Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
wiley +1 more source
Minimal definable graphs of definable chromatic number at least three
Forum of Mathematics, Sigma, 2021 We show that there is a Borel graph on a standard Borel space of Borel chromatic number three that admits a Borel homomorphism to every analytic graph on a standard Borel space of Borel chromatic number at least three. Moreover, we characterize the Borel
Raphaël Carroy +3 more
doaj +1 more source
Nikolai Luzin and the problem of existence in mathematics
Revista Integración, 2017 This paper presents excerpts of the discussion about the problem of existence for functions in each one of Baire’ s classes. First, it sets up the historical problem, introducing four existential categories, and then it shows Luzin’ s position and ...
Andrés Chaves, Luis C. Recalde
doaj +1 more source
MEASURABLE REALIZATIONS OF ABSTRACT SYSTEMS OF CONGRUENCES
Forum of Mathematics, Sigma, 2020 An abstract system of congruences describes a way of partitioning a space into finitely many pieces satisfying certain congruence relations. Examples of abstract systems of congruences include paradoxical decompositions and $n$-divisibility of actions ...
CLINTON T. CONLEY +2 more
doaj +1 more source
Game characterizations and lower cones in the Weihrauch degrees [PDF]
Logical Methods in Computer Science, 2019 We introduce a parametrized version of the Wadge game for functions and show that each lower cone in the Weihrauch degrees is characterized by such a game.
Hugo Nobrega, Arno Pauly
doaj +1 more source
Feedback computability on Cantor space [PDF]
Logical Methods in Computer Science, 2019 We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show that the feedback
Nathanael L. Ackerman +2 more
doaj +1 more source