Singular compactifications: the order structure
HTML articles powered by AMS MathViewer
- by Richard E. Chandler and Gary D. Faulkner
- Proc. Amer. Math. Soc. 100 (1987), 377-382
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884483-2
- PDF | Request permission
Abstract:
This paper investigates the order structure of the collection of singular compactifications of a locally compact Hausdorff space. In particular we will prove several theorems showing that $\beta X$ is the supremum of these simpler compactifications.References
- P. S. Alexandroff and P. Urysohn, Memoire sur les espaces topologiques compacts, Verh. Nederl. Akad. Wetensch. Afd. Natuurk. 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 Jr., Mappings with prescribed singular sets, Nieuw Arch. Wisk. (3) 17 (1969), 200–203. MR 256364
- George L. Cain Jr., Properties of $\beta X-X$ for locally connected generalized continua, Proc. Amer. Math. Soc. 79 (1980), no. 2, 311–315. MR 565361, DOI 10.1090/S0002-9939-1980-0565361-9
- 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
- Richard E. Chandler, Gary D. Faulkner, Josephine P. Guglielmi, and Margaret C. Memory, Generalizing the Alexandroff-Urysohn double circumference construction, Proc. Amer. Math. Soc. 83 (1981), no. 3, 606–608. MR 627703, DOI 10.1090/S0002-9939-1981-0627703-6
- W. W. Comfort, Retractions and other continuous maps from $\beta X$ onto $\beta X\sbs X$, Trans. Amer. Math. Soc. 114 (1965), 1–9. MR 185571, DOI 10.1090/S0002-9947-1965-0185571-9
- John B. Conway, Projections and retractions, Proc. Amer. Math. Soc. 17 (1966), 843–847. MR 195048, DOI 10.1090/S0002-9939-1966-0195048-9 Josephine P. Guglielmi, Compactifications with singular remainders, Ph. D. Thesis, North Carolina State University, 1986.
- G. T. Whyburn, Compactification of mappings, Math. Ann. 166 (1966), 168–174. MR 200905, DOI 10.1007/BF01361445
- G. T. Whyburn, Dynamic topology, Amer. Math. Monthly 77 (1970), 556–570. MR 264635, DOI 10.2307/2316732
- Eric K. van Douwen, Retractions from $\beta X$ onto $\beta X-X$, General Topology Appl. 9 (1978), no. 2, 169–173. MR 515003
Bibliographic Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 100 (1987), 377-382
- MSC: Primary 54D35; Secondary 54C10, 54D40
- DOI: https://doi.org/10.1090/S0002-9939-1987-0884483-2
- MathSciNet review: 884483