Completely regular and $\omega$-regular spaces
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- by D. C. Kent and G. D. Richardson PDF
- Proc. Amer. Math. Soc. 82 (1981), 649-652 Request permission
Abstract:
The completely regular convergence spaces are characterized as those spaces having symmetric compactifications. The $\omega$-regular convergence spaces are those which have regular compactifications.References
- Ernst Binz, Continuous convergence on $C(X)$, Lecture Notes in Mathematics, Vol. 469, Springer-Verlag, Berlin-New York, 1975. MR 0461418, DOI 10.1007/BFb0088826
- H.-P. Butzmann and B. Mรผller, Topological $c$-embedded spaces, General Topology and Appl. 6 (1976), no.ย 1, 17โ20. MR 388309, DOI 10.1016/0016-660X(76)90003-9
- A. C. Cochran and R. B. Trail, Regularity and complete regularity for convergence spaces, Topology Conference (Virginia Polytech. Inst. and State Univ., Blacksburg, Va., 1973) Lecture Notes in Math., Vol. 375, Springer, Berlin, 1974, pp.ย 64โ70. MR 0355931
- G. D. Richardson and D. C. Kent, The regularity series of a convergence space, Bull. Austral. Math. Soc. 13 (1975), no.ย 1, 21โ44. MR 377795, DOI 10.1017/S0004972700024229
- D. C. Kent and G. D. Richardson, The regularity series of a convergence space. II, Bull. Austral. Math. Soc. 15 (1976), no.ย 2, 223โ243. MR 433367, DOI 10.1017/S0004972700022590
- D. Kent, K. McKennon, G. Richardson, and M. Schroder, Continuous convergence in $C(X)$, Pacific J. Math. 52 (1974), 457โ465. MR 370482, DOI 10.2140/pjm.1974.52.457
- G. D. Richardson, A Stone-ฤech compactification for limit spaces, Proc. Amer. Math. Soc. 25 (1970), 403โ404. MR 256336, DOI 10.1090/S0002-9939-1970-0256336-1
- G. D. Richardson and D. C. Kent, Regular compactifications of convergence spaces, Proc. Amer. Math. Soc. 31 (1972), 571โ573. MR 286074, DOI 10.1090/S0002-9939-1972-0286074-2
- G. D. Richardson and D. C. Kent, A note on $C_{c}(X)$, Proc. Amer. Math. Soc. 49 (1975), 441โ445. MR 370483, DOI 10.1090/S0002-9939-1975-0370483-X
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 649-652
- MSC: Primary 54A20; Secondary 54D15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0614896-X
- MathSciNet review: 614896