Strong collectionwise normality and M. E. Rudin’s Dowker space

Hart, K. P.

doi:10.1090/S0002-9939-1981-0630058-4

Strong collectionwise normality and M. E. Rudin’s Dowker space
HTML articles powered by AMS MathViewer

by K. P. Hart PDF

Proc. Amer. Math. Soc. 83 (1981), 802-806 Request permission

Abstract:

stract. We investigate the relationship between strong collectionwise normality and some other separation properties. The conclusion is that in general there is none. In addition some properties of M. E. Rudin’s Dowker space are found.

References

C. R. Borges, Four generalizations of stratifiable spaces, General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971) Academia, Prague, 1972, pp. 73–76. MR 0362245

Sur une problème de M. Dieudonné

234

H. H. Corson, Examples relating to normality in topological spaces, Trans. Amer. Math. Soc. 99 (1961), 205–211. MR 124024, DOI 10.1090/S0002-9947-1961-0124024-7
R. W. Heath, D. J. Lutzer, and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481–493. MR 372826, DOI 10.1090/S0002-9947-1973-0372826-2
John L. Kelley, General topology, Graduate Texts in Mathematics, No. 27, Springer-Verlag, New York-Berlin, 1975. Reprint of the 1955 edition [Van Nostrand, Toronto, Ont.]. MR 0370454
M. J. Mansfield, Some generalizations of full normality, Trans. Amer. Math. Soc. 86 (1957), 489–505. MR 93753, DOI 10.1090/S0002-9947-1957-0093753-5
Mary Ellen Rudin, A normal space $X$ for which $X\times I$ is not normal, Fund. Math. 73 (1971/72), no. 2, 179–186. MR 293583, DOI 10.4064/fm-73-2-179-186
H. L. Shapiro and F. A. Smith, Paracompactness in uniform spaces, Topology Proc. 3 (1978), no. 1, 179–197 (1979). MR 540489

Simultaneous extension of continuous functions