Geodesic
An Internal Characterization of Realcompactness
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 439-444

Voir la notice de l'article provenant de la source Cambridge University Press

A space is realcompact if it is a homeomorph of a closed subspace of a product of real lines. Many external characterizations of realcompactness have appeared, but there seems to be no simple internal characterization. We provide such a characterization in terms of the existence of a collection of covers of a certain type and use it to examine realcompact extensions of a space and to characterize the Q-closure of a space in a compac tification.A structure on X is a collection of covers of X that forms a filter under refinement ordering; the members of a structure are called gauges. A balanced refinement of a gauge a is a gauge β with cardinal not greater than that of a such that for each B ∈ β there is A ∈ α such that {A, X – B} is also a gauge; thus a balanced refinement is certainly a refinement. 
Harris, Douglas. An Internal Characterization of Realcompactness. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 439-444. doi: 10.4153/CJM-1971-046-4
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