Singular sets and remainders

Cain, George L.; Chandler, Richard E.; Faulkner, Gary D.

doi:10.1090/S0002-9947-1981-0628452-5

Singular sets and remainders
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by George L. Cain, Richard E. Chandler and Gary D. Faulkner PDF

Trans. Amer. Math. Soc. 268 (1981), 161-171 Request permission

Abstract:

This paper characterizes the singular sets of several traditional classes of continuous mappings associated with compactifications. By relating remainders of compactifications to singular sets of mappings with compact range, new results are obtained about each.

References

G. R. Blakley, J. Gerlits, and K. D. Magill Jr., A class of spaces with identical remainders, Studia Sci. Math. Hungar. 6 (1971), 117–122. MR 362229
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 Jr., Continuous preimages of spaces with finite compactifications, Canad. Math. Bull. 24 (1981), no. 2, 177–180. MR 619443, DOI 10.4153/CMB-1981-028-2
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
Eng Ung Choo, Accumulation points of continuous real-valued functions and compactifications, Canad. Math. Bull. 20 (1977), no. 1, 47–52. MR 448286, DOI 10.4153/CMB-1977-009-7
K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835
Peter A. Loeb, A minimal compactification for extending continuous functions, Proc. Amer. Math. Soc. 18 (1967), 282–283. MR 216468, DOI 10.1090/S0002-9939-1967-0216468-0
K. D. Magill Jr., More on remainders of spaces in compactifications, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 449–451 (English, with Russian summary). MR 268854
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
A. K. Steiner and E. F. Steiner, Graph closures and metric compactifications of $N$, Proc. Amer. Math. Soc. 25 (1970), 593–597. MR 264614, DOI 10.1090/S0002-9939-1970-0264614-5
Gordon Thomas Whyburn, Analytic topology, American Mathematical Society Colloquium Publications, Vol. XXVIII, American Mathematical Society, Providence, R.I., 1963. MR 0182943
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