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On equivalence of unbounded metric spaces at infinity
Viktoriia Bilet, Oleksiy Dovgoshey
Let be an unbounded metric space. To investigate the asymptotic behavior of at infinity, one can consider a sequence of rescaling metric spaces $(X, \frac{1}{r_n}…
Ultrametrics and complete multipartite graphs
Viktoriia Bilet, Oleksiy Dovgoshey, Yuriy Kononov
We describe the class of graphs for which all metric spaces with diametrical graphs belonging to this class are ultrametric. It is shown that a metric space is ultrametric…
Finite asymptotic clusters of metric spaces
Viktoriia Bilet, Oleksiy Dovgoshey
Let be an unbounded metric space and let be a sequence of positive real numbers tending to infinity. A pretangent space $Ω_{\infty, \tilde…
Asymptotic structure of general metric spaces at infinity
Viktoriia Bilet, Oleksiy Dovgoshey
Let be an unbounded metric space and be a scaling sequence of positive real numbers tending to infinity. We define the pretangent space $Ω_…
Uniform boundedness of pretangent spaces and local strong one-side porosity
Viktoriia Bilet, Oleksiy Dovgoshey
Let (X,d,p) be a pointed metric space. A pretangent space to X at p is a metric space consisting of some equivalence classes of convergent to p sequences (x_n), x_n \in X, whose de…
Pretangent spaces with nonpositive and nonnegative Aleksandrov curvature
Viktoriia Bilet, Oleksiy Dovgoshey
We find conditions under which the pretangent spaces to general metric spaces have the nonpositive Aleksandrov curvature or nonnegative one. The infinitesimal structure of general…