Geodesic
Discrete Subsets of Proximity Spaces
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 225-230

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

The distinct Hausdorff compactifications δX of a completely regular (Hausdorff) space X are in one-one correspondence with the admissible proximity relations δ on X, or alternatively, with the admissible totally bounded uniform structures for X. (See [1], [2].) Thus, δX is the Smirnov compactification of (X, δ). Generalized uniform structures for X will be described by means of pseudometrics on X (cf. [5], [7], [13]). Let where is in the proximity class π(δ) associated with (X, δ). Then a subset S of X is σ-discrete of gauge if , for all x, y ∈ S where x ≠ y. 
Mattson, Don A. Discrete Subsets of Proximity Spaces. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 225-230. doi: 10.4153/CJM-1979-023-3
@article{10_4153_CJM_1979_023_3,
     author = {Mattson, Don A.},
     title = {Discrete {Subsets} of {Proximity} {Spaces}},
     journal = {Canadian journal of mathematics},
     pages = {225--230},
     year = {1979},
     volume = {31},
     number = {2},
     doi = {10.4153/CJM-1979-023-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-023-3/}
}
TY  - JOUR
AU  - Mattson, Don A.
TI  - Discrete Subsets of Proximity Spaces
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 225
EP  - 230
VL  - 31
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-023-3/
DO  - 10.4153/CJM-1979-023-3
ID  - 10_4153_CJM_1979_023_3
ER  - 
%0 Journal Article
%A Mattson, Don A.
%T Discrete Subsets of Proximity Spaces
%J Canadian journal of mathematics
%D 1979
%P 225-230
%V 31
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-023-3/
%R 10.4153/CJM-1979-023-3
%F 10_4153_CJM_1979_023_3

[1] 1. Alfsen, E. M. and Fenstad, J. E., A note on completion and compactification, Math. Scand. 8 (1960), 97–104. Google Scholar

[2] 2. Alfsen, E. M. and Njastad, O., Proximity and generalized uniformity, Fund. Math. 52 (1963), 235–252. Google Scholar

[3] 3. Chandler, R. E. and Cellar, R., The compactifications to which an element of C*(X) extends, Proc. Amer. Math. Soc. 38 (1973), 637–639. Google Scholar

[4] 4. Gantner, T., Extensions of uniformly continuous pseudometrics, Trans. Amer. Math. Soc. 132 (1968), 147–157. Google Scholar

[5] 5. Gillman, L. and Jerison, M., Rings of continuous functions, (The University Series in Higher Math., Princeton, N.J., 1960). Google Scholar

[6] 6. Harris, D., An internal characterization of realcompactness, Can. J. Math. 23 (1971), 439–444. Google Scholar

[7] 7. Leader, S., On pseudometrics for generalized uniform structures, Proc. Amer. Math. Soc. 16 (1965), 493–495. Google Scholar

[8] 8. Mattson, D., Real maximal round filters in proximity spaces, Fund. Math. 78 (1973), 183–188. Google Scholar

[9] 9. Mattson, D., On completions of proximity and uniform spaces, Coll. Math. 38 (1977), 55–62. Google Scholar

[10] 10. Njastad, O., On p-systems and p-functions, Norske Vid. Selsk. Skr. 1 (1968), 1–10. Google Scholar

[11] 11. Njastad, O., On real-valued proximity mappings, Math. Annale. 154 (1964), 413–419. Google Scholar

[12] 12. Reed, E. E. and Thron, W. J., n-bounded uniformities, Trans. Amer. Math. Soc. 141 (1969), 71–77. Google Scholar

[13] 13. Thron, W. S., Topological structures, (Holt, Rinehart, and Winston, New York, 1966). Google Scholar

Cité par Sources :