On singular $H$-closed extensions
HTML articles powered by AMS MathViewer
- by Kavita Srivastava PDF
- Proc. Amer. Math. Soc. 120 (1994), 295-300 Request permission
Abstract:
Introducing the notion of singular $H$-closed extensions of a locally $H$-closed space, we obtain a necessary and sufficient condition for a semiregular $H$-closed extension to be singular.References
- Bernhard Banaschewski, Extensions of topological spaces, Canad. Math. Bull. 7 (1964), 1–22. MR 161293, DOI 10.4153/CMB-1964-001-5
- George L. Cain Jr., Compact and related mappings, Duke Math. J. 33 (1966), 639–645. MR 200903 —, Compactness of certain closed mappings, Notices Amer. Math. Soc. 14 (1967), 374.
- George L. Cain Jr., Mappings with prescribed singular sets, Nieuw Arch. Wisk. (3) 17 (1969), 200–203. MR 256364
- 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 and Fu-Chien Tzung, Remainders in Hausdorff compactifications, Proc. Amer. Math. Soc. 70 (1978), no. 2, 196–202. MR 487981, DOI 10.1090/S0002-9939-1978-0487981-3
- Richard E. Chandler and Gary D. Faulkner, Singular compactifications: the order structure, Proc. Amer. Math. Soc. 100 (1987), no. 2, 377–382. MR 884483, DOI 10.1090/S0002-9939-1987-0884483-2
- 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
- R. F. Dickman Jr., Unified spaces and singular sets for mappings of locally compact spaces, Fund. Math. 62 (1968), 103–123. MR 227951, DOI 10.4064/fm-62-2-103-123
- Gary D. Faulkner, Compactifications whose remainders are retracts, Proc. Amer. Math. Soc. 103 (1988), no. 3, 984–988. MR 947694, DOI 10.1090/S0002-9939-1988-0947694-4
- Mike Girou, Properties of locally H-closed spaces, Proc. Amer. Math. Soc. 113 (1991), no. 1, 287–295. MR 1047001, DOI 10.1090/S0002-9939-1991-1047001-5 Josephine P. Guglielmi, Compactifications with singular remainders, Ph.D. Thesis, North Carolina State Univ., 1986.
- Jack R. Porter and Charles Votaw, $H$-closed extensions. I, General Topology and Appl. 3 (1973), 211–224. MR 326659, DOI 10.1016/0016-660X(72)90013-X
- Jack R. Porter and Charles Votaw, $H$-closed extensions. II, Trans. Amer. Math. Soc. 202 (1975), 193–209. MR 365493, DOI 10.1090/S0002-9947-1975-0365493-7
- Jack R. Porter and R. Grant Woods, Extensions and absolutes of Hausdorff spaces, Springer-Verlag, New York, 1988. MR 918341, DOI 10.1007/978-1-4612-3712-9
- G. T. Whyburn, On compactness of mappings, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 1426–1431. MR 176450, DOI 10.1073/pnas.52.6.1426
- G. T. Whyburn, Compactification of mappings, Math. Ann. 166 (1966), 168–174. MR 200905, DOI 10.1007/BF01361445
- Albert Wilansky, Topology for analysis, Ginn (A Xerox company), Waltham, Mass.-Toronto, Ont.-London, 1970. MR 0451181
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 295-300
- MSC: Primary 54D35; Secondary 54C10, 54D40
- DOI: https://doi.org/10.1090/S0002-9939-1994-1172962-6
- MathSciNet review: 1172962