We study families of Axiom A skew products with the transversality condition and in particular, the Hausdorff dimension of their fibers, by using thermodynamical formalism. The maps we consider can be non-invertible, and the study of their dynamics is influenced greatly by this fact. We introduce and employ probability measures (constructed from equilibrium measures on the natural extension), w...

We answer a question of I. Juhasz by showing that MA +¬ CH does not imply that every compact ccc space of countable π-character is separable. The space constructed has the additional property that it does not map continuously onto Iω1 .

Let 0 < a < b < 1 and let T be the doubling map. Set J (a, b) := {x ∈ [0, 1] : Tx / ∈ (a, b), n ≥ 0}. In this paper we completely characterize the holes (a, b) for which any of the following scenarios holds: (i) J (a, b) contains a point x ∈ (0, 1); (ii) J (a, b) ∩ [δ, 1− δ] is infinite for any fixed δ > 0; (iii) J (a, b) is uncountable of zero Hausdorff dimension; (iv) J (a, b) is of positive ...

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping and f ∈ F , let Mπ(f)(x) := π(x)f(x). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be a mu...

Let V be a system of weights on a completely regular Hausdorff space and let B(E) be the topological vector space of all continuous linear operators on a Hausdorff topological vector space E. Let CV0(X,E) and CVb(X,E) be the nonlocally convex weighted spaces of continuous functions. In the present paper, we characterize compact multiplication operators Mψ on CV0 (X,E) ( or CVb(X,E)) induced by ...

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X,...

In this paper, we present a new approach for hand-written character and digit recognitions based on shape descriptor and the Hausdorff Context. We start at finding the corresponding points between two shapes by using a modified shape context. We then use these correspondences as key geometric points for shape alignment with the Thin Plate Spline (TPS) model. After the transformation has been ap...

We investigate which definable separable metric spaces are countable dense homogeneous (CDH). We prove that a Borel CDH space is completely metrizable and give a complete list of zero-dimensional Borel CDH spaces. We also show that for a Borel X ⊆ 2 the following are equivalent: (1) X is Gδ in 2 ω , (2) X is CDH and (3) X is homeomorphic to 2 or to ω . Assuming the Axiom of Projective Determina...

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $ma...

We study the spectrum of forcing notions between the iterations of σ-closed followed by ccc forcings and the proper forcings. This includes the hierarchy of α-proper forcings for indecomposable countable ordinals α, the Axiom A forcings and forcings completely embeddable into an iteration of a σ-closed followed by a ccc forcing. For the latter class, we present an equivalent characterization in...