Properties of Stone-Čech compactifications of discrete spaces
HTML articles powered by AMS MathViewer
- by Nancy M. Warren PDF
- Proc. Amer. Math. Soc. 33 (1972), 599-606 Request permission
Abstract:
Let $\beta N$ be the Stone-Čech compactification of the integers N. It is shown that p is a P-point of $\beta N - N$, then $\beta N - N - \{ p\}$ is not normal. Let D be an uncountable discrete set and ${E_0}$ be the set of points in $\beta D - D$ in the closures of countable subsets of D It is shown that there is a two-valued continuous function on ${E_0}$ which cannot be extended continuously to $\beta D$.References
- W. W. Comfort and S. Negrepontis, Homeomorphs of three subspaces of $\beta {\bf {\rm }N}\backslash {\bf {\rm }N}$, Math. Z. 107 (1968), 53–58. MR 234422, DOI 10.1007/BF01111048
- N. J. Fine and L. Gillman, Extension of continuous functions in $\beta N$, Bull. Amer. Math. Soc. 66 (1960), 376–381. MR 123291, DOI 10.1090/S0002-9904-1960-10460-0
- Mary Ellen Rudin, Types of ultrafilters, Topology Seminar (Wisconsin, 1965) Ann. of Math. Studies, No. 60, Princeton Univ. Press, Princeton, N.J., 1966, pp. 147–151. MR 0216451 G. Kurepa, Ensembles linéaires et une classe de tableaux ramifiés (tableaux ramifiés de M. Aronszajn), Publ. Math. Univ. Belgrade 6 (1937), 129-160.
- F. Burton Jones, On certain well-ordered monotone collections of sets, J. Elisha Mitchell Sci. Soc. 69 (1953), 30–34. MR 56052
- 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
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 599-606
- MSC: Primary 54D35
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292035-X
- MathSciNet review: 0292035