Topological size of scrambled sets

Topological Size of Sets of Partial Recursive Functions

Relativized Topological Size of Sets of Partial Recursive Functions

Calude, C., Relativized topological size of sets of partial recursive functions (Note), Theoretical Computer Science 87 (1991) 347-352. In [ 11, a recursive topology on the set of unary partial recursive functions was introduced and recursive variants of Baire topological notions of nowhere dense and meagre sets were defined. These tools were used to measure the size of some classes of partial ...

Scrambled Sets of Continuous Maps of 1-dimensional Polyhedra

Let K be a 1-dimensional simplicial complex in R3 without isolated vertexes, X = |K| be the polyhedron of K with the metric dK induced by K, and f : X → X be a continuous map. In this paper we prove that if K is finite, then the interior of every scrambled set of f in X is empty. We also show that if K is an infinite complex, then there exist continuous maps from X to itself having scrambled se...

FUZZY BOUNDED SETS AND TOTALLY FUZZY BOUNDED SETS IN I-TOPOLOGICAL VECTOR SPACES

In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

Dimension of Stable Sets and Scrambled Sets in Positive Finite Entropy Systems

We study dimension of stable sets and scrambled sets of a dynamical system with positive finite entropy. We show that there is a measure-theoretically “large” set containing points whose sets of “hyperbolic points” (i.e., points lying in the intersections of the closures of the stable and unstable sets) admit positive Bowen dimension entropies, which, under a continuum hypothesis, also contains...