Characterizations of metric spaces by the use of their midsets: intervals
Characterizations of snowflake metric spaces.
Characterizations of some bitopological separation axioms in terms of - closure operator
Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. (Short Communication).
Characterizations of uniformity-dependent dimension functions
Characterizations of -stratifiable spaces
Characterizations of σ-spaces
Characterizing cell-decomposable metrics.
Characterizing strong countable-dimensionality in terms of Baire category
C(K) spaces which cannot be uniformly embedded into c₀(Γ)
We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.
Classifying homogeneous ultrametric spaces up to coarse equivalence
For every metric space X we introduce two cardinal characteristics and describing the capacity of balls in X. We prove that these cardinal characteristics are invariant under coarse equivalence, and that two ultrametric spaces X,Y are coarsely equivalent if . This implies that an ultrametric space X is coarsely equivalent to an isometrically homogeneous ultrametric space if and only if . Moreover, two isometrically homogeneous ultrametric spaces X,Y are coarsely equivalent if and only if ...
Cleavability and divisibility over developable spaces
Some results on cleavability theory are presented. We also show some new [16]'s results.
Cliff functions - a tool for treating sequences of composed functions.
Cliff functions - a tool for treating sequences of composed functions. (Short Communication).
Clone properties of topological spaces
Clone properties are the properties expressible by the first order sentence of the clone language. The present paper is a contribution to the field of problems asking when distinct sentences of the language determine distinct topological properties. We fully clarify the relations among the rigidity, the fix-point property, the image-determining property and the coconnectedness.
Closed, continuous images of complete metric spaces
Closed copies of the rationals
Closed mappings on complete metric spaces
Coarea integration in metric spaces
Let be a metric space with a doubling measure, be a boundedly compact metric space and be a Lebesgue precise mapping whose upper gradient belongs to the Lorentz space , . Let be a set of measure zero. Then for -a.e. , where is the -dimensional Hausdorff measure and is the -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.