Generalizing the Alexandroff-Urysohn double circumference construction
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- by Richard E. Chandler, Gary D. Faulkner, Josephine P. Guglielmi and Margaret C. Memory
- Proc. Amer. Math. Soc. 83 (1981), 606-608
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627703-6
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Abstract:
This paper is a unification of the "Alexandroff-Urysohn Double Circumference Construction", the one-point compactification, the Steiner and Steiner remainder theorem, and Whyburn’s Unified Space. All of these are shown to be different aspects of a single construction.References
- P. S. Alexandroff and P. Urysohn, Mémoire sur les espaces topologique compacts, Verh. Nederl. Akad. Wetensch. Afd. Naturk. Sect. I 14 (1929), 1-96.
- George L. Cain Jr., Compact and related mappings, Duke Math. J. 33 (1966), 639–645. MR 200903
- George L. Cain, Richard E. Chandler, and Gary D. Faulkner, Singular sets and remainders, Trans. Amer. Math. Soc. 268 (1981), no. 1, 161–171. MR 628452, DOI 10.1090/S0002-9947-1981-0628452-5
- R. Engelking, On the double circumference of Alexandroff, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 629–634 (English, with Russian summary). MR 0239564
- A. K. Steiner and E. F. Steiner, Compactifications as closures of graphs, Fund. Math. 63 (1968), 221–223. MR 238270, DOI 10.4064/fm-63-2-221-223
- G. T. Whyburn, A unified space for mappings, Trans. Amer. Math. Soc. 74 (1953), 344–350. MR 52762, DOI 10.1090/S0002-9947-1953-0052762-9
- G. T. Whyburn, Compactification of mappings, Math. Ann. 166 (1966), 168–174. MR 200905, DOI 10.1007/BF01361445
Bibliographic Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 83 (1981), 606-608
- MSC: Primary 54D35; Secondary 54C20
- DOI: https://doi.org/10.1090/S0002-9939-1981-0627703-6
- MathSciNet review: 627703