A simple proof of Hausdorff's theorem on extending metrics
A subset of metric preserving functions.
A theorem on expansions into inverse systems of metric spaces
A uniquely homogeneous space need not be a topological group
A universal separable metric locally finite-dimensional space
Algebraic and topological structures on the set of mean functions and generalization of the AGM mean
We present new structures and results on the set of mean functions on a given symmetric domain in ℝ². First, we construct on a structure of abelian group in which the neutral element is the arithmetic mean; then we study some symmetries in that group. Next, we construct on a structure of metric space under which is the closed ball with center the arithmetic mean and radius 1/2. We show in particular that the geometric and harmonic means lie on the boundary of . Finally, we give two theorems...
Almost locatedness in uniform spaces
A weak form of the constructively important notion of locatedness is lifted from the context of a metric space to that of a uniform space. Certain fundamental results about almost located and totally bounded sets are then proved.
An observation on spaces with a zeroset diagonal
We say that a space has the discrete countable chain condition (DCCC for short) if every discrete family of nonempty open subsets of is countable. A space has a zeroset diagonal if there is a continuous mapping with , where . In this paper, we prove that every first countable DCCC space with a zeroset diagonal has cardinality at most .
Another note on countable Boolean algebras
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
Approximative limit and related notions
Some notions of limit weaker than the topological one are studied.
Archimedean and geodetical biequivalences
Are EC-spaces AE(metrizable)?
Around Katětov's metrization theorem
Asymptotically equal generalized distances: induced topologies and -energy of a curve.
on spaces of homogeneous type: a density result on - spaces.
Ball versus distance convexity of metric spaces.
Best constants for metric space inversion inequalities
For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X o The constant 2 is best possible.
Best simultaneous approximations
In this paper we study simultaneous approximation of real-valued functions in and give a generalization of some related results.
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces