Geodesic
Homeomorphic Sets of Remote Points
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 495-502

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

Let X be a completely regular Hausdorff space, and let βX denote the Stone-Čech compactification of X. A point p ∈ βX is called a remote point of βX if p does not belong to the βX-closure of any discrete subspace of X. Remote points were first defined and studied by Fine and Gillman, who proved that if the continuum hypothesis is assumed then the set of remote points of β R((β Q) is dense in β R – R(β Q – Q ) (R denotes the space of reals, Q the space of rationals). Assuming the continuum hypothesis, Plank has proved that if X is a locally compact, non-compact, separable metric space without isolated points, then βX has a set of remote points that is dense in βX – X. Robinson has extended this result by dropping the assumption that X is separable. 
Woods, R. Grant. Homeomorphic Sets of Remote Points. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 495-502. doi: 10.4153/CJM-1971-052-1
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