A new fixed-point theorem for contractive mappings.
A new iterative method for common fixed points of a finite family of nonexpansive mappings.
A non-regular Toeplitz flow with preset pure point spectrum
Given an arbitrary countable subgroup of the torus, containing infinitely many rationals, we construct a strictly ergodic 0-1 Toeplitz flow with pure point spectrum equal to . For a large class of Toeplitz flows certain eigenvalues are induced by eigenvalues of the flow Y which can be seen along the aperiodic parts.
A Non-standard Version of the Borsuk-Ulam Theorem
E. Pannwitz showed in 1952 that for any n ≥ 2, there exist continuous maps φ:Sⁿ→ Sⁿ and f:Sⁿ→ ℝ² such that f(x) ≠ f(φ(x)) for any x∈ Sⁿ. We prove that, under certain conditions, given continuous maps ψ,φ:X→ X and f:X→ ℝ², although the existence of a point x∈ X such that f(ψ(x)) = f(φ(x)) cannot always be assured, it is possible to establish an interesting relation between the points f(φ ψ(x)), f(φ²(x)) and f(ψ²(x)) when f(φ(x)) ≠ f(ψ(x)) for any x∈ X, and a non-standard version of the Borsuk-Ulam...
A non-symmetric generalization of the Borsuk -Ulam theorem
A note on almost periodic points and minimal sets in - and -spaces.
A note on asymptotic contractions.
A note on coclones of topological spaces
The clone of a topological space is known to have a strictly more expressive first-order language than that of the monoid of continuous self-maps. The current paper studies coclones of topological spaces (i.e. clones in the category dual to that of topological spaces and continuous maps) and proves that, in contrast to clones, the first-order properties of coclones cannot express anything more than those of the monoid, except for the case of discrete and indiscrete spaces.
A note on cocycles in ergodic theory
A note on compact groups, acting on R-trees
A note on complementarity problem.
A note on countably determined and distinguishable sets
A note on embeddings manifolds into topological groups preserving dimensions
A note on Fixed Point Mappings with contracting orbital diameters.
A note on fixed point theorem of Schauder type with applications
A note on fixed points of a selfmap of an extremally disconnected space
A note on f.p.p. and
In [3], Kinoshita defined the notion of and he proved that each compact AR has In [4], Yonezawa gave some examples of not locally connected continua with f.p.p., but without In general, for each n=1,2,..., there is an n-dimensional continuum with f.p.p., but without such that is locally (n-2)-connected (see [4, Addendum]). In this note, we show that for each n-dimensional continuum X which is locally (n-1)-connected, X has f.p.p. if and only if X has
A note on ideals of compact sets
Solecki has shown that a broad natural class of ideals of compact sets can be represented through the ideal of nowhere dense subsets of a closed subset of the hyperspace of compact sets. In this note we show that the closed subset in this representation can be taken to be closed upwards.
A note on generic chaos
We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.
A note on hyperspaces and the fixed point property