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Selections on Ψ -spaces

Michael Hrušák, Paul J. Szeptycki, Artur Hideyuki Tomita (2001)

Commentationes Mathematicae Universitatis Carolinae

We show that if 𝒜 is an uncountable AD (almost disjoint) family of subsets of ω then the space Ψ ( 𝒜 ) does not admit a continuous selection; moreover, if 𝒜 is maximal then Ψ ( 𝒜 ) does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.

Selivanovski hard sets are hard

Janusz Pawlikowski (2015)

Fundamenta Mathematicae

Let H Z 2 ω . For n ≥ 2, we prove that if Selivanovski measurable functions from 2 ω to Z give as preimages of H all Σₙ¹ subsets of 2 ω , then so do continuous injections.

Semicopulas: characterizations and applicability

Fabrizio Durante, José Quesada-Molina, Carlo Sempi (2006)

Kybernetika

We characterize some bivariate semicopulas and, among them, the semicopulas satisfying a Lipschitz condition. In particular, the characterization of harmonic semicopulas allows us to introduce a new concept of depedence between two random variables. The notion of multivariate semicopula is given and two applications in the theory of fuzzy measures and stochastic processes are given.

Semi-monotone sets

Saugata Basu, Andrei Gabrielov, Nicolai Vorobjov (2013)

Journal of the European Mathematical Society

A coordinate cone in n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of n , definable in an o-minimal structure over the reals, such that its intersection with any translation of any coordinate cone is connected. This notion can be viewed as a generalization of convexity. Semi-monotone sets have a number of interesting geometric and combinatorial properties. The main result of the paper is that every semi-monotone...

Semiproper ideals

Hiroshi Sakai (2005)

Fundamenta Mathematicae

We say that an ideal I on κ λ is semiproper if the corresponding poset I is semiproper. In this paper we investigate properties of semiproper ideals on κ λ .

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