Geodesic
Nowhere Dense Subsets of Metric Spaces with Applications to Stone-Cech Compactifications
Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 622-630

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

Let X be a metric space. Assume either that X is locally compact or that X has no more than countably many isolated points. It is proved that if F is a nowhere dense subset of X, then it is regularly nowhere dense (in the sense of Katětov) and hence is contained in the topological boundary of some regular-closed subset of X. This result is used to obtain new properties of the remote points of the Stone-Čech compactification of a metric space without isolated points.Let βX denote the Stone-Čech compactification of the completely regular Hausdorff space X. Fine and Gillman [3] define a point p of βX to be remote if p is not in the βX-closure of a discrete subset of X. 
Porter, Jack R.; Woods, R. Grant. Nowhere Dense Subsets of Metric Spaces with Applications to Stone-Cech Compactifications. Canadian journal of mathematics, Tome 24 (1972) no. 4, pp. 622-630. doi: 10.4153/CJM-1972-057-3
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[1] 1. Dugundji, J., Topology (Allyn and Bacon, Mass., 1965). Google Scholar

[2] 2. Fine, N. J. and Gillman, L., Extensions of continuous functions in f3N, Bull. Amer. Math. Soc. 66 (1960), 376-381. Google Scholar

[3] 3. Fine, N. J. and Gillman, L., Remote points in 0R, Proc. Amer. Math. Soc. 13 (1962), 29–36. Google Scholar

[4] 4. Gillman, L. and Jerison, M., Rings of continuous functions, University Series in Higher Mathematics (Van Nostrand, Princeton, New Jersey, 1960). Google Scholar

[5] 5. Katětov, M., On the equivalence of certain types of extensions of topological spaces, Časopis Pěst. Mat. Fys. 72 (1947), 101–106. Google Scholar

[6] 6. Mandelker, M., Prime z-ideal structure of C(R), Fund. Math. 63 (1968), 145–166. Google Scholar

[7] 7. Mandelker, M., Round z-filters and round subsets of (3X, Israel J. Math. 7 (1969), 1–8. Google Scholar

[8] 8. Plank, D. L., On a class of subalgebras of C﹛X) with applications to βX-X, Fund. Math. 64 (1969), 41–52. Google Scholar

[9] 9. Sikorski, R., Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Band 25 (Academic Press, New York; Springer-Verlag, Berlin and New York, 1964). Google Scholar

[10] 10. Woods, R. G., Co-absolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545–560. Google Scholar

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