$C$-embedded subsets of products
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- by N. Noble PDF
- Proc. Amer. Math. Soc. 31 (1972), 613-614 Request permission
Abstract:
It is shown that each dense subset of ${R^\mathfrak {n}}$ is $z$-embedded, from which it follows that a dense subset is $C$-embedded if and only if it is ${G_\delta }$-dense. These results extend to, for example, all products of separable metric spaces.References
- H. H. Corson, Normality in subsets of product spaces, Amer. J. Math. 81 (1959), 785–796. MR 107222, DOI 10.2307/2372929 A. Hager, $C -$-, ${C^\ast } -$-, and $z$-embedding (to appear).
- Robert W. Heath and Ernest A. Michael, A property of the Sorgenfrey line, Compositio Math. 23 (1971), 185–188. MR 287515 N. Noble, Realcompactness of function spaces (to appear).
- N. Noble and Milton Ulmer, Factoring functions on Cartesian products, Trans. Amer. Math. Soc. 163 (1972), 329–339. MR 288721, DOI 10.1090/S0002-9947-1972-0288721-2
- K. A. Ross and A. H. Stone, Products of separable spaces, Amer. Math. Monthly 71 (1964), 398–403. MR 164314, DOI 10.2307/2313241 M. Ulmer, Continuous functions on product spaces, Doctoral Dissertation, Wesleyan University, Middletown, Conn., 1970.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 613-614
- DOI: https://doi.org/10.1090/S0002-9939-1972-0284978-8
- MathSciNet review: 0284978