Selection from Upper Semi-Continuous Compact-Valued Mappings.
We show that if is an uncountable AD (almost disjoint) family of subsets of then the space does not admit a continuous selection; moreover, if is maximal then does not even admit a continuous selection on pairs, answering thus questions of T. Nogura.
Let . For n ≥ 2, we prove that if Selivanovski measurable functions from to Z give as preimages of H all Σₙ¹ subsets of , then so do continuous injections.
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.
A coordinate cone in is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is an open bounded subset of , 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...
We say that an ideal I on is semiproper if the corresponding poset is semiproper. In this paper we investigate properties of semiproper ideals on .