RT Journal Article
T1 The Samuel realcompactification
A1 Garrido Carballo, María Isabel
A1 Meroño Moreno, Ana Soledad
AB For a uniform space (X, μ), we introduce a realcompactification of X by means of the family Uμ(X) of all the real-valued uniformly continuous functions on X, in the same way that the known Samuel compactification of the space is given by U∗μ(X) the set of all the bounded functions in Uμ(X). We will call it “the Samuel realcompactification” by several resemblances to the Samuel compactification. In this paper, we present different ways to construct such realcompactification as well as we study the corresponding problem of knowing when a uniform space is Samuel realcompact, that is, when it (topologically) coincides with its Samuelrealcompactification. At this respect, we obtain as main result a theorem of Katětov–Shirota type, given in terms of a property of completeness, recently introduced by the authors, called Bourbaki-completeness.
PB Elsevier
SN 0166-8641
YR 2018
FD 2018
LK https://hdl.handle.net/20.500.14352/100629
UL https://hdl.handle.net/20.500.14352/100629
LA eng
NO Garrido, M. Isabel, y Ana S. Meroño. «The Samuel Realcompactification». Topology and Its Applications, vol. 241, junio de 2018, pp. 150-61. DOI.org (Crossref), https://doi.org/10.1016/j.topol.2018.03.033.
DS Docta Complutense
RD 30 jun 2025