• Corpus ID: 249375414

# Completeness, Closedness and Metric Reflections of Pseudometric Spaces

@inproceedings{Bilet2022CompletenessCA,
title={Completeness, Closedness and Metric Reflections of Pseudometric Spaces},
author={Viktoriia Bilet and Oleksiy Dovgoshey},
year={2022}
}
• Published 3 June 2022
• Mathematics
. It is well-known that a metric space ( X, d ) is complete iﬀ the set X is closed in every metric superspace of ( X, d ) . For a given pseudometric space ( Y, ρ ) , we describe the maximal class CEC ( Y, ρ ) of superspaces of ( Y, ρ ) such that ( Y, ρ ) is complete if and only if Y is closed in every ( Z, ∆) ∈ CEC ( Y, ρ ) . We also introduce the concept of pseudoisometric spaces and prove that spaces are pseudoisometric iﬀ their metric reﬂections are isometric. The last result implies that a…

## References

SHOWING 1-10 OF 26 REFERENCES
A relation between porosity convergence and pretangent spaces
• Philosophy
Publications de l'Institut Math?matique (Belgrade)
• 2021
The convergence of porosity is one of the relatively new concept in Mathematical analysis. It is completely structurally different from the other convergence concepts. Here we give a relation
On equivalence of unbounded metric spaces at infinity
• Mathematics
• 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
Uniqueness of spaces pretangent to metric spaces at infinity
• Mathematics
Journal of Mathematical Sciences
• 2019
We find the necessary and sufficient conditions under which an unbounded metric space $$X$$ has, at infinity, a unique pretangent space $$\Omega^{X}_{\infty,\tilde{r}}$$ for every scaling sequence
Finite Spaces Pretangent to Metric Spaces at Infinity
• Mathematics
Journal of Mathematical Sciences
• 2019
Let X be an unbounded metric space, and let $$\tilde{r}$$ be a sequence of positive real numbers tending to infinity. We define the pretangent space $${\Omega}_{\infty, \tilde{r}}^X$$ to X at
Combinatorial properties of ultrametrics and generalized ultrametrics
• O. Dovgoshey
• Mathematics
Bulletin of the Belgian Mathematical Society - Simon Stevin
• 2020
Let $X$, $Y$ be sets and let $\Phi$, $\Psi$ be mappings with domains $X^{2}$ and $Y^{2}$ respectively. We say that $\Phi$ and $\Psi$ are combinatorially similar if there are bijections $f \colon Combinatorial characterization of pseudometrics • Mathematics Acta Mathematica Hungarica • 2020 Let X, Y be sets and let $$\Phi, \Psi$$ Φ , Ψ be mappings with the domains X 2 and Y 2 respectively. We say that $$\Phi$$ Φ is combinatorially similar to $$\Psi$$ Ψ if there are bijections$$f \colon On the metric reflection of a pseudometric space in ZF • Mathematics • 2015 We show: (i) The countable axiom of choice$\mathbf{CAC}\$ is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially