Perfectly normal compact spaces are continuous images of 𝛽𝐍_{𝐍}

Perfectly normal compact spaces are continuous images of $\beta \mathbf {N}_{\mathbf {N}}$
HTML articles powered by AMS MathViewer

by Teodor C. Przymusiński PDF

Proc. Amer. Math. Soc. 86 (1982), 541-544 Request permission

Every perfectly normal compact space is a continuous image of ${N^ * } = \beta N\backslash N$.

References

Concerning Parovičenko’s theorem

Eric K. van Douwen and Teodor C. Przymusiński, Separable extensions of first countable spaces, Fund. Math. 105 (1979/80), no. 2, 147–158. MR 561588, DOI 10.4064/fm-105-2-147-158
Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779

Some remarks on embeddings of Boolean algebras and topological spaces

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
I. I. Parovičenko, On a universal bicompactum of weight $\aleph$, Dokl. Akad. Nauk SSSR 150 (1963), 36–39. MR 0150732
B. Šapirovskiĭ, Canonical sets and character. Density and weight in bicompacta, Dokl. Akad. Nauk SSSR 218 (1974), 58–61 (Russian). MR 0383332