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- W3103081930 abstract "Two non-empty sets $A,B$ of a metric space $(X,d)$ are called parallel if $d(a,B)=d(A,B)=d(A,b)$ for any points $ain A$ and $bin B$. Answering a question posed on Mathoverflow, we prove that for a cover $mathcal C$ of a metrizable space $X$ the following conditions are equivalent: (i) the topology of $X$ is generated by a metric $d$ such that any two sets $A,Binmathcal C$ are parallel; (ii) the cover $mathcal C$ is disjoint, lower semicontinuous and upper semicontinuous." @default.
- W3103081930 created "2020-11-23" @default.
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- W3103081930 date "2019-01-03" @default.
- W3103081930 modified "2023-10-09" @default.
- W3103081930 title "A parallel metrization theorem" @default.
- W3103081930 doi "https://doi.org/10.1007/s40879-018-00311-6" @default.
- W3103081930 hasPublicationYear "2019" @default.
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