Semigroup of Contractions of Wreath Products of Metric Spaces
In this paper semigroups of contractions of metric spaces are considered. The semigroup of contractions of the wreath product of metric spaces is calculated.
Separation properties for self-conformal sets
For a one-to-one self-conformal contractive system on with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to . We give a simple proof of this result as well as discuss some further properties related to the separation condition.
Sobre las isometrías de los grupos y anillos reticulados.
El contenido de este trabajo tiene un objetivo fundamental: el estudio, clasificación y caracterización de las isometrías de un grupo reticulado. Se introducen los conceptos de grupo de isometrías M(G) de un grupo reticulado G, grupo de simetrías homogéneas H(G) y traslaciones T(G). Se estudia primero el caso elemental de los grupos totalmente ordenados y utilizando luego las representaciones de los grupos (y f-anillos) en un producto de totalmente ordenados, se introduce el concepto de conjunto...
Some common fixed point theorems in complete -fuzzy metric spaces.
Some problems concerning stability of fixed points
Some questions on the composition factor property for atomic mappings.
Some results on fixed and coincidence points of couples of maps in metric spaces
Some results on fixed points and their continuity
Some results on -spaces
We present several results related to -spaces where is a finite cardinal or ; we consider products and some constructions that lead from spaces of these classes to other spaces of similar classes.
Some similarity between contractions and Kannan mappings.
Spaces with a locally countable -network.
Spaces with countable -networks
In this paper, we prove that a space is a sequentially-quotient -image of a metric space if and only if has a point-star -network consisting of -covers. By this result, we prove that a space is a sequentially-quotient -image of a separable metric space if and only if has a countable -network, if and only if is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...
Spaces With -Locally Finite Lindelöf sn-Networks
Striped structures of stable and unstable sets of expansive homeomorphisms and a theorem of K. Kuratowski on independent sets
We investigate striped structures of stable and unstable sets of expansive homeomorphisms and continuum-wise expansive homeomorphisms. The following theorem is proved: if f : X → X is an expansive homeomorphism of a compact metric space X with dim X > 0, then the decompositions and of X into stable and unstable sets of f respectively are uncountable, and moreover there is σ (= s or u) and ϱ > 0 such that there is a Cantor set C in X with the property that for each x ∈ C, contains a nondegenerate...
Strongly paracompact metrizable spaces
Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.
The lifting property for classes of mappings.
The nonexistence of expansive homeomorphisms of chainable continua
A homeomorphism f:X → X of a compactum X with metric d is expansive if there is c > 0 such that if x, y ∈ X and x ≠ y, then there is an integer n ∈ ℤ such that . In this paper, we prove that if a homeomorphism f:X → X of a continuum X can be lifted to an onto map h:P → P of the pseudo-arc P, then f is not expansive. As a corollary, we prove that there are no expansive homeomorphisms on chainable continua. This is an affirmative answer to one of Williams’ conjectures.
The nonexistence of expansive homeomorphisms of dendroids
The solenoids are the only circle-like continua that admit expansive homeomorphisms
A homeomorphism h:X → X of a compactum X is expansive provided that for some fixed c > 0 and any distinct x, y ∈ X there exists an integer n, dependent only on x and y, such that d(hⁿ(x),hⁿ(y)) > c. It is shown that if X is a circle-like continuum that admits an expansive homeomorphism, then X is homeomorphic to a solenoid.
Triangle functions and composition of probability distribution functions.
The equations of left and right distributivity of composition of distribution functions over triangle functions are solved in a restricted domain.