Geodesic
Two R-Closed Spaces
Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 286-292

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

Throughout this paper all hypothesized spaces are T1. A regular space is called R-closed[11](regular-closed [7] or, equivalently, regular-complete [2]) provided that it is a closed subset of any regular space in which it can be embedded. A regular space (X, I) is called minimal regular [2; 4] if there exists no regular topology on X which is strictly weaker than J. We shall call a regular space X strongly minimal regular provided that each point x ∈ X has a fundamental system of neighbourhoods such that for every V ∈ , X\V is an R-closed space.In §2 we note that a strongly minimal regular space is minimal regular, but we do not know if the converse holds. M. P. Berri and R. H. Sorgenfrey [4] proved that a minimal regular space is R-closed, and Horst Herrlich [7] gave an example of an R-closed space that is not minimal regular. 
Stephenson, R. M. Two R-Closed Spaces. Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 286-292. doi: 10.4153/CJM-1972-023-5
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