The metric confluent images of half-lines and lines
The minimal ideals of a multiplicative and additive subsemigroup of ßN.
The minimum dimension of a residual ANR
The minimum tree for a given zero-entropy period.
The minimum uniform compactification of a metric space
It is shown that associated with each metric space (X,d) there is a compactification of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of are presented, and a detailed study of the structure of is undertaken. This culminates in a topological characterization of the outgrowth , where is Euclidean n-space with its usual metric.
The Möbius-Pompeiu metric property.
The monad induced by the hom-functor in the category of topological spaces and its associated Eilenberg-Moore algebras.
The monomorphism semigroup of S(X).
The multicores in metric spaces and their application in fixed point theory
This paper discusses the notion, the properties and the application of multicores, i.e. some compact sets contained in metric spaces.
The Nachbin compactification via convergence ordered spaces.
The neighborhood complex of an infinite graph.
The Niemytzki plane is -metrizable
We prove that the Niemytzki plane is -metrizable and we try to explain the differences between the concepts of a stratifiable space and a -metrizable space. Also, we give a characterisation of -metrizable spaces which is modelled on the version described by Chigogidze.
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 nonexistence of universal metric flows
We consider dynamical systems of the form where is a compact metric space and is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract -limit sets, answering a question by Will Brian.
The Non-Simplicity of Certain Categories of Topological Spaces.
The notion of closedness in topological categories
In [1], various generalizations of the separation properties, the notion of closed and strongly closed points and subobjects of an object in an arbitrary topological category are given. In this paper, the relationship between various generalized separation properties as well as relationship between our separation properties and the known ones ([4], [5], [7], [9], [10], [14], [16]) are determined. Furthermore, the relationships between the notion of closedness and strongly closedness are investigated...
The notion of -shape
The notions of w-net and Y-compact space viewed under infinitesimal microscope.