Topological essentiality for multivalued weighted mappings
Topological Galois spaces
Topological groups of divisibility
Topological Interpretation of Rough Sets
Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in [14]) and...
Topological invariance of the Collet–Eckmann property for S-unimodal maps
We prove that if f, g are smooth unimodal maps of the interval with negative Schwarzian derivative, conjugated by a homeomorphism of the interval, and f is Collet-Eckmann, then so is g.
Topological Markov chains with dicyclic dimension group.
Topological multidimensional van der Waerden theorem
Topological orbit equivalence and C*-crossed products.
Topological representations of quasiordered sets.
Topological semigroups and Kirk's question
Topological semivector spaces: convexity and fixed point theory.
Topological sequence entropy for maps of the circle
A continuous map of the interval is chaotic iff there is an increasing sequence of nonnegative integers such that the topological sequence entropy of relative to , , is positive ([FS]). On the other hand, for any increasing sequence of nonnegative integers there is a chaotic map of the interval such that ([H]). We prove that the same results hold for maps of the circle. We also prove some preliminary results concerning topological sequence entropy for maps of general compact metric...
Topological size of scrambled sets
A subset S of a topological dynamical system (X,f) containing at least two points is called a scrambled set if for any x,y ∈ S with x ≠ y one has and , d being the metric on X. The system (X,f) is called Li-Yorke chaotic if it has an uncountable scrambled set. These notions were developed in the context of interval maps, in which the existence of a two-point scrambled set implies Li-Yorke chaos and many other chaotic properties. In the present paper we address several questions about scrambled...
Topological structure of solution sets: current results
Topological vector space-valued cone metric spaces and fixed point theorems.
Topologically Transitive Subsets of Piecewise Monotonic Maps, Which Contain no Periodic Points.
Topologies associated to some decision statistical functions
Topologies on free monoids induced by closure operators of a special type
Topologies on groups determined by right cancellable ultrafilters
For every discrete group , the Stone-Čech compactification of has a natural structure of a compact right topological semigroup. An ultrafilter , where , is called right cancellable if, given any , implies . For every right cancellable ultrafilter , we denote by the group endowed with the strongest left invariant topology in which converges to the identity of . For any countable group and any right cancellable ultrafilters , we show that is homeomorphic to if and only if...
Topologies on the Group of Self Homeomorphisms of the Cantor Set