# On equivalence of unbounded metric spaces at infinity

@inproceedings{Bilet2021OnEO, title={On equivalence of unbounded metric spaces at infinity}, author={Viktoriia Bilet and Oleksiy Dovgoshey}, year={2021} }

Let (X, d) be an unbounded metric space. To investigate the asymptotic behavior of (X, d) at infinity, one can consider a sequence of rescaling metric spaces (X, 1 rn d) generated by given sequence (rn)n∈N of positive reals with rn → ∞. Metric spaces that are limit points of the sequence (X, 1 rn d)n∈N will be called pretangent spaces to (X, d) at infinity. We found the necessary and sufficient conditions under which two given unbounded subspaces of (X, d) have the same pretangent spaces at…

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