RT Journal Article
T1 A result concerning the Lipschitz realcompactification of the product of two metric spaces
A1 Garrido Carballo, María Isabel
A1 Meroño Moreno, Ana Soledad
AB For a metric space (X, d), we consider the so-called Lipschitz realcompactification of X, denoted by H(Lipd(X)). In this note we give a result concerning the equality H(Lipd+ρ(X × Y )) = H(Lipd(X)) × H(Lipρ(Y )) for the product of the two metric spaces (X, d) and (Y, ρ). More precisely, we prove that such equality holds if and only if H(Lipd(X)) = X or H(Lipρ(Y )) = Y , where X and Y denote the completion of X and Y respectively, or equivalently, if and only if the Lipschitz realcompactification of one of the factors X or Y is as simple as possible. We also point out that our result is, in fact, a true generalization of a known theorem by Woods about the Samuel compactification of the product of two metric spaces.
PB Elsevier
SN 0166-8641
YR 2023
FD 2023
LK https://hdl.handle.net/20.500.14352/128489
UL https://hdl.handle.net/20.500.14352/128489
LA eng
NO Garrido, M. Isabel, y Ana S. Meroño. «A Result Concerning the Lipschitz Realcompactification of the Product of Two Metric Spaces». Topology and Its Applications, vol. 339, noviembre de 2023, p. 108585. DOI.org (Crossref), https://doi.org/10.1016/j.topol.2023.108585.
NO Ministerio de Economía y Competitividad (España)
DS Docta Complutense
RD 21 mar 2026