Let M be the collection of all intersections of balls, considered as a subset of the hyperspace H of all closed, convex and bounded sets of a Banach space, furnished with the Hausdorff metric. We prove that M is uniformly very porous if and only if the space fails the Mazur intersection property.

We prove that if a finite algebra A generates a congruence distributive variety then the subalgebras of the powers of A satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.

In this paper fixed point theorems for maps with nonempty convex values and having the local intersection property are given. As applications several minimax inequalities are obtained.

In this work, we prove that metric spaces with uniform normal structure have a kind of intersection property, which is equivalent to reflexivity in Banach spaces.

We prove that the finite representation property holds for representation by partial functions for the signature consisting of composition, intersection, antidomain and range. It follows that the finite representation property holds for any expansion of this signature with the fixset, preferential union, maximum iterate and opposite operators. The proof shows that for all these signatures the s...

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

Several cases of the monomial conjecture are proved. An equivalent form of the direct summand conjecture is discussed. Let (A,m, k) be a noetherian local ring of dimension n, m its maximal ideal and k = A/m. The Monomial Conjecture (henceforth MC) of Hochster asserts that, given any system of parameters (henceforth s.o.p.) x1, . . . , xn of A, (x1x2 . . . xn) t−1 / ∈ (x1, . . . , xn) ∀t > 0. Ho...

We constructively prove that for every LTL formula φ, the smallest safety property containing the property expressed by φ is also expressible in LTL. It immediately follows that LTL admits the safety-liveness decomposition: any property expressed by an LTL formula is equivalent to the intersection of a safety property and a liveness property, both of them expressible in LTL. Our proof is based ...