Remainders of compactifications and their relation to a quotient lattice of the topology

Faulkner, G. D.; Vipera, M. C.

doi:10.1090/S0002-9939-1994-1231033-0

Remainders of compactifications and their relation to a quotient lattice of the topology
HTML articles powered by AMS MathViewer

by G. D. Faulkner and M. C. Vipera PDF

Proc. Amer. Math. Soc. 122 (1994), 931-942 Request permission

Abstract:

If $\alpha X$ is a compactification of a locally compact space X, then the remainder associated with $\alpha X$ is the space $\alpha X\backslash X$. Frequently spaces which are quite different may have families of remainders which are related. This must be reflected somehow in the structure of the spaces. This paper studies one possible formulation of that similarity and its consequences.

References

Garrett Birkhoff, Lattice theory, 3rd ed., American Mathematical Society Colloquium Publications, Vol. XXV, American Mathematical Society, Providence, R.I., 1967. MR 0227053
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
A. Caterino, G. D. Faulkner, and M. C. Vipera, Construction of compactifications using essential semilattice homomorphisms, Proc. Amer. Math. Soc. 116 (1992), no. 3, 851–860. MR 1111215, DOI 10.1090/S0002-9939-1992-1111215-7
W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267
Miroslav Katětov, On $H$ closed extensions of topological spaces, Časopis Pěst. Mat. Fys. 72 (1947), 17–32 (English, with Czech summary). MR 0022069
Kenneth D. Magill Jr., The lattice of compactifications of a locally compact space, Proc. London Math. Soc. (3) 18 (1968), 231–244. MR 229209, DOI 10.1112/plms/s3-18.2.231
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