Compactifications with discrete remainders

Hatzenbuhler, James P.; Mattson, Don A.

doi:10.1090/S0002-9939-1995-1301028-8

Compactifications with discrete remainders
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by James P. Hatzenbuhler and Don A. Mattson PDF

Proc. Amer. Math. Soc. 123 (1995), 2927-2934 Request permission

Abstract:

Conditions are obtained which characterize when a space has a Hausdorff compactification with a discrete remainder. A characterization is also given for when the minimal perfect compactification of a 0-space has a discrete remainder. It is shown that a metric space has a compactification with a discrete remainder if and only if it is rimcompact. In general, however, for a space to have a compactification with a discrete remainder, it is not necessary that the space be rimcompact.

References

G. L. Cain, Countable compactifications, General topology and its relations to modern analysis and algebra, VI (Prague, 1986) Res. Exp. Math., vol. 16, Heldermann, Berlin, 1988, pp. 69–75. MR 952592
Richard E. Chandler, Hausdorff compactifications, Lecture Notes in Pure and Applied Mathematics, Vol. 23, Marcel Dekker, Inc., New York-Basel, 1976. MR 0515002
Beverly Diamond, Some properties of almost rimcompact spaces, Pacific J. Math. 118 (1985), no. 1, 63–77. MR 783017, DOI 10.2140/pjm.1985.118.63
Beverly Diamond, James Hatzenbuhler, and Don Mattson, On when a $O$-space is rimcompact, Topology Proc. 13 (1988), no. 2, 189–202. MR 1053696
James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
W. Fleissner, J. Kulesza, and R. Levy, Remainders of normal spaces, Topology Appl. 49 (1993), no. 2, 167–174. MR 1206223, DOI 10.1016/0166-8641(93)90042-C
Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199, DOI 10.1007/978-1-4615-7819-2

Paracompact and metrizable remainders

J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323, DOI 10.1090/surv/012
J. R. McCartney, Maximum zero-dimensional compactifications, Proc. Cambridge Philos. Soc. 68 (1970), 653–661. MR 270340, DOI 10.1017/s0305004100076647
Marlon C. Rayburn, On Hausdorff compactifications, Pacific J. Math. 44 (1973), 707–714. MR 317277, DOI 10.2140/pjm.1973.44.707

Some questions in the theory of bicompactifications

58

Toshiji Terada, On countable discrete compactifications, General Topology and Appl. 7 (1977), no. 3, 321–327. MR 500840
Jun Terasawa, Spaces $\textbf {N}\cup {\cal R}$ and their dimensions, Topology Appl. 11 (1980), no. 1, 93–102. MR 550876, DOI 10.1016/0166-8641(80)90020-6