Ordered spaces all of whose continuous images are normal
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- by William Fleissner and Ronnie Levy PDF
- Proc. Amer. Math. Soc. 105 (1989), 231-235 Request permission
Abstract:
Some spaces, such as compact Hausdorff spaces, have the property that every regular continuous image is normal. In this paper, we look at such spaces. In particular, it is shown that if a normal space has finite Stone-Čech remainder, then every continuous image is normal. A consequence is that every continuous image of a Dedekind complete linearly ordered topological space of uncountable cofinality and coinitiality is normal. The normality of continuous images of other ordered spaces is also discussed.References
- James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass., 1966. MR 0193606
- 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
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 105 (1989), 231-235
- MSC: Primary 54F05; Secondary 54D15
- DOI: https://doi.org/10.1090/S0002-9939-1989-0973846-4
- MathSciNet review: 973846