Resolutions of $H$-closed spaces
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- by Louis M. Friedler PDF
- Proc. Amer. Math. Soc. 71 (1978), 309-312 Request permission
Abstract:
It is shown that every Hausdorff space X is the perfect, irreducible, continuous image of a Hausdorff space $\tilde X$ which has a basis with open closures. Further, $w(\tilde X) \leqslant w(X)$, where $w(\tilde X)$ represents the weight of X, and if X is H-closed then $\tilde X$ is also H-closed. A corollary of this result is that if $f:X \to Y$ is a continuous map of the H-closed space X onto the semi-regular Hausdorff space Y, then $w(Y) \leqslant w(X)$.References
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M. P. Berri, J. R. Porter and R. M. Stephenson, Jr., A survey of minimal topological spaces, Proc. Kanpur Top. Conf. 1968, General Topology and its Relations to Modern Analysis and Algebra III, Academic Press, N. Y., 1970.
- T. O. Vinson Jr. and R. F. Dickman Jr., Inverse limits and absolutes of $H$-closed spaces, Proc. Amer. Math. Soc. 66 (1977), no. 2, 351–358. MR 482660, DOI 10.1090/S0002-9939-1977-0482660-X
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- Louis M. Friedler and Dix H. Pettey, Inverse limits and mappings of minimal topological spaces, Pacific J. Math. 71 (1977), no. 2, 429–448. MR 464158, DOI 10.2140/pjm.1977.71.429
- Andrew M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), 482–489. MR 121775
- S. Iliadis, Absolutes of Hausdorff spaces, Dokl. Akad. Nauk SSSR 149 (1963), 22–25 (Russian). MR 0157354
- C. T. Liu and G. E. Strecker, Concerning almost realcompactifications, Czechoslovak Math. J. 22(97) (1972), 181–190. MR 303507, DOI 10.21136/CMJ.1972.101088
- J. Mioduszewski and L. Rudolf, $H$-closed and extremally disconnected Hausdorff spaces, Dissertationes Math. (Rozprawy Mat.) 66 (1969), 55. MR 256353
- S. Iliadis, Absolutes of Hausdorff spaces, Dokl. Akad. Nauk SSSR 149 (1963), 22–25 (Russian). MR 0157354
- John Rainwater, A note on projective resolutions, Proc. Amer. Math. Soc. 10 (1959), 734–735. MR 123290, DOI 10.1090/S0002-9939-1959-0123290-8
- Dona Papert Strauss, Extremally disconnected spaces, Proc. Amer. Math. Soc. 18 (1967), 305–309. MR 210066, DOI 10.1090/S0002-9939-1967-0210066-0
- Giovanni Viglino, Extensions of functions and spaces, Trans. Amer. Math. Soc. 179 (1973), 61–69. MR 322785, DOI 10.1090/S0002-9947-1973-0322785-3
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 71 (1978), 309-312
- MSC: Primary 54D25
- DOI: https://doi.org/10.1090/S0002-9939-1978-0493965-1
- MathSciNet review: 0493965