# 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} }

. 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…

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