Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Compactifications whose remainders are retracts


Author: Gary D. Faulkner
Journal: Proc. Amer. Math. Soc. 103 (1988), 984-988
MSC: Primary 54D35; Secondary 54C10, 54D40
DOI: https://doi.org/10.1090/S0002-9939-1988-0947694-4
MathSciNet review: 947694
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper is concerned with compactifications in which the remainder is a (neighborhood) retract. Two theorems which characterize such compactifications are proved here. One of the characterizations is in terms of singular functions and the other in terms of projections on spaces of continuous real valued functions.


References [Enhancements On Off] (What's this?)

  • [1] George L. Cain, Jr., Compact and related mappings, Duke Math. J. 33 (1966), 639-645. MR 0200903 (34:789)
  • [2] -, Mappings with prescribed singular sets, Nieuw. Arch. Wisk. (3) 17 (1969), 200-203. MR 0256364 (41:1020)
  • [3] George L. Cain, Jr., Richard E. Chandler, and Gary D. Faulkner, Singular sets and remainders, Trans. Amer. Math. Soc. 268 (1981), 161-171. MR 628452 (82k:54039)
  • [4] Richard E. Chandler, Gary D. Faulkner, Josephine P. Guglielmi, and Margaret Memory, Generalizing the Alexandroff-Urysohn double circumference construction, Proc. Amer. Math. Soc. 83 (1981), 606-608. MR 627703 (82m:54019)
  • [5] Richard E. Chandler and F. C. Tzung, Remainders in Hausdorff compactifications, Proc. Amer. Math. Soc. 70 (1978), 196-202. MR 0487981 (58:7560)
  • [6] W. W. Comfort, Retractions and other continuous maps from $ \beta X$ to $ \beta X\backslash X$, Trans. Amer. Math. Soc. 114 (1965), 1-9. MR 0185571 (32:3035)
  • [7] John B. Conway, Projections and retractions, Proc. Amer. Math. Soc. 17 (1966), 843-847. MR 0195048 (33:3253)
  • [8] D. W. Dean, Projections in certain continuous function spaces, Canad. J. Math. 14 (1962), 385-401. MR 0144191 (26:1738)
  • [9] -, Subspaces of $ C(H)$ which are direct factors of $ C(H)$, Proc. Amer. Math. Soc. 16 (1965), 237-242. MR 0173137 (30:3352)
  • [10] N. Dunford and J. T. Schwartz, Linear operators, Wiley, New York, 1957.
  • [11] Josephine P. Guglielmi, Compactifications with singular remainders, Ph.D. Thesis, North Carolina State Univ., 1986.
  • [12] H. Elton Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, New York, 1974. MR 0493279 (58:12308)
  • [13] K. D. Magill, Jr., $ N$-point compactifications, Amer. Math. Monthly. Soc. 72 (1965), 1075-1081. MR 0185572 (32:3036)
  • [14] R. S. Phillips, On linear transformations, Trans. Amer. Math. Soc. 48 (1940), 516-541. MR 0004094 (2:318c)
  • [15] A. Sobczyk, Projection of the space $ (m)$ on its subspace $ ({c_0})$, Bull. Amer. Math. Soc. 47 (1941), 938-947. MR 0005777 (3:205f)
  • [16] G. T. Whyburn, Compactifications of mappings, Math. Ann. 166 (1966), 168-174. MR 0200905 (34:791)
  • [17] Eric K. van Douwen, Retractions from $ \beta X$ onto $ \beta X\backslash X$, General Topology Appl. 9 (1978), 169-173. MR 0515003 (58:24192)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54D35, 54C10, 54D40

Retrieve articles in all journals with MSC: 54D35, 54C10, 54D40


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947694-4
Keywords: Compactification, remainder, singular mappings, projections
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society