Function algebras and the lattice
Proc. Amer. Math. Soc. 127 (1999), 1863-1871
Primary 54D35, 54C35, 54D40, 46E25
February 17, 1999
Full-text PDF Free Access
Similar Articles |
Abstract: We provide some conditions as to when for two locally compact spaces and (where is the lattice of all Hausdorff compactifications of ). More specifically, we prove that if and only if . Using this result, we prove several extensions to the case where is embedded as a sub-lattice of and to where and are not locally compact.
One major contribution is in the use of function algebra techniques. The use of these techniques makes the extensions simple and clean and brings new tools to the subject.
M. Aarts and P.
van Emde Boas, Continua as remainders in compact extensions,
Nieuw Arch. Wisk. (3) 15 (1967), 34–37. MR 0214033
E. Chandler, Hausdorff compactifications, Marcel Dekker, Inc.,
New York-Basel, 1976. Lecture Notes in Pure and Applied Mathematics, Vol.
0515002 (58 #24191)
A. Firby, Lattices and compactifications. I, II, III, Proc.
London Math. Soc. (3) 27 (1973), 22–50; ibid. (3) 27
(1973), 51–60; ibid. (3) 27 (1973), 61–68. MR 0324651
Gillman and Meyer
Jerison, Rings of continuous functions, Springer-Verlag, New
York-Heidelberg, 1976. Reprint of the 1960 edition; Graduate Texts in
Mathematics, No. 43. MR 0407579
D. Magill Jr., A note on compactifications, Math. Z.
94 (1966), 322–325. MR 0203681
D. Magill Jr., The lattice of compactifications of a locally
compact space, Proc. London Math. Soc. (3) 18 (1968),
231–244. MR 0229209
C. Rayburn, On Hausdorff compactifications, Pacific J. Math.
44 (1973), 707–714. MR 0317277
Joseph Rotman, An Introduction to the Theory of Groups, Wm. C. Brown Publishers, Dubuque, Iowa, 1988.
R. Porter and R.
Grant Woods, Extensions and absolutes of Hausdorff spaces,
Springer-Verlag, New York, 1988. MR 918341
Thrivikraman, On the lattices of compactifications, J. London
Math. Soc. (2) 4 (1972), 711–717. MR 0296902
- J. M. Aarts and P. Van Emde Boas, Continua as Remainders in Compact Extensions, Nieuw Archief voor Wiskunde 3, XV (1967), 34-37. MR 35:4885
- Richard Chandler, Hausdorff Compactifications, Lecture notes in pure and applied mathematics 23, Marcel Dekker, New York, 1976. MR 58:24191
- P. A. Firby, Lattices and Compactifications I, II, and III. Proc. London Math Soc. 27 (1973), p. 22-68. MR 48:3001
- L. Gillman and M. Jerison, Rings of Continuous Functions, Graduate Texts in Mathematics 43, Springer-Verlag, New York, 1976. MR 53:11352
- K. D. Magill, Jr., A note on compactifications, Math. Zeitschr. 94 (1966), p. 322-325. MR 34:3530
- K. D. Magill, Jr., The lattice of compactifications of a locally compact space, Proc. London Math. Soc. 18 (1968), p. 231-244. MR 37:4783
- Marlon C. Rayburn, On Hausdorff Compactifications, Pac. J. Math. 44 (1973), 707-714. MR 47:5824
- Joseph Rotman, An Introduction to the Theory of Groups, Wm. C. Brown Publishers, Dubuque, Iowa, 1988.
- Jack R. Porter and R. Grant Woods, Extensions and Absolutes of Hausdorff Spaces, Springer-Verlag, New York, 1988. MR 89b:54003
- T. Thrivikraman, On the lattices of compactifications, J. London Math Soc. 4 (1972), p. 711-717. MR 45:5961
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (1991):
Retrieve articles in all journals
with MSC (1991):
Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication:
Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
lattice of compactifications,
rings of continuous functions
Received by editor(s):
December 10, 1996
Received by editor(s) in revised form:
September 22, 1997
February 17, 1999
© Copyright 1999
American Mathematical Society