Tangency relations for sets in some classes in generalized metric spaces
The Banach–Mazur game and σ-porosity
It is well known that the sets of the first category in a metric space can be described using the so-called Banach-Mazur game. We will show that if we change the rules of the Banach-Mazur game (by forcing the second player to choose large balls) then we can describe sets which can be covered by countably many closed uniformly porous sets. A characterization of σ-very porous sets and a sufficient condition for σ-porosity are also given in the terminology of games.
The box product of countably many metrizable spaces need not be normal
The convexity of the subset space of a metric space
The dimension of metrizable subspaces of Eberlein compacta and Eberlein compactifications of metrizable spaces
We prove that every Baire subspace Y of c₀(Γ) has a dense metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.
The dual group of a dense subgroup
Throughout this abstract, is a topological Abelian group and is the space of continuous homomorphisms from into the circle group in the compact-open topology. A dense subgroup of is said to determine if the (necessarily continuous) surjective isomorphism given by is a homeomorphism, and is determined if each dense subgroup of determines . The principal result in this area, obtained independently by L. Außenhofer and M. J. Chasco, is the following: Every metrizable group is...
The inverse image of a metric space under a biquotient compact mapping
The Kannan's fixed point theorem in a cone rectangular metric space.
The Kantorovič-Rubinstein distance
The Kantorovič-Rubinstein distance
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 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 number of metrizable spaces
The positive cone of a Banach lattice. Coincidence of topologies and metrizability
Let be a Banach lattice, and denote by its positive cone. The weak topology on is metrizable if and only if it coincides with the strong topology if and only if is Banach-lattice isomorphic to for a set . The weak topology on is metrizable if and only if is Banach-lattice isomorphic to a -space, where is a metrizable compact space.
The universal separable metric space of Urysohn and isometric embeddings thereof in Вanach spaces
This paper is an investigation of the universal separable metric space up to isometry U discovered by Urysohn. A concrete construction of U as a metric subspace of the space C[0,1] of functions from [0,1] to the reals with the supremum metric is given. An answer is given to a question of Sierpiński on isometric embeddings of U in C[0,1]. It is shown that the closed linear span of an isometric copy of U in a Banach space which contains the zero of the Banach space is determined up to linear isometry....
Theory of equidistance and betweenness relations in regular metric spaces
There is no universal totally disconnected space
Timan's Formula for the Deviation of Hölder Functions.
Topological spaces admitting a unique fractal structure
Each homeomorphism from the n-dimensional Sierpiński gasket into itself is a similarity map with respect to the usual metrization. Moreover, the topology of this space determines a kind of Haar measure and a canonical metric. We study spaces with similar properties. It turns out that in many cases, "fractal structure" is not a metric but a topological phenomenon.