An ultrafilter p on ω is said to be discrete if, given any function f:ω→X completely regular Hausdorff space, there an A∈p such that f(A) discrete. Basic properties of ultrafilters are studied. Three intermediate classes spaces R1⊂R2⊂R3 between the class F-spaces and van Douwen's βω-spaces introduced. It proved no product infinite compact R2-spaces homogeneous; moreover, under assumption d=c, h...

ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes into ordered categories. It an extension of TRI-B that uses limiting profiles, instead one, delimit each category. In previous paper we have characterized the partitions can be obtained with TRI-nB, using simple axiom called linearity. The simplicity this characterization crucially rests possibility use as ...

We prove that the algorithm of [13] for approximating the Hausdorff dimension of dynamically defined Cantor sets, using periodic points of the underlying dynamical system, can be used to establish completely rigorous high accuracy bounds on the dimension. The effectiveness of these rigorous estimates is illustrated for Cantor sets consisting of continued fraction expansions with restricted digi...

We show how to calculate the finite-state dimension (equivalently, the finite-state compressibility) of a saturated sets X consisting of all infinite sequences S over a finite alphabet Σm satisfying some given condition P on the asymptotic frequencies with which various symbols from Σm appear in S. When the condition P completely specifies an empirical probability distribution π over Σm, i.e., ...

The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using diff...

Work on calculations with simplicial and cubical groups in AXIOM was carried out using loan equipment and software from IBM UK and guidance from L A Lambe. We report on the results of this work, and present the AXIOM code written by the second author during this period. This includes an implementation of the monoids which model cubes and simplices, together with a new AXIOM category of near-rin...

In 1969, Hirsch posed the following problem: given a diffeomorphism f : N → N , and a compact invariant hyperbolic set Λ of f , describe the topology of Λ and the dynamics of f restricted to Λ. We solve the problem where Λ = M is a closed 3-manifold: if M is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions....

We investigate the connection between the dynamical Borel-Cantelli and waiting time results. We prove that if a system has the dynamical BorelCantelli property, then the time needed to enter for the first time in a sequence of small balls scales as the inverse of the measure of the balls. Conversely if we know the waiting time behavior of a system we can prove that certain sequences of decreasi...