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On compactification of mappings

Published online by Cambridge University Press:  20 January 2009

P. A. Firby
P. A. Firby
Affiliation:
THe University, Exeter
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If X and Y are Tychonoff spaces then the continuous function f mapping X onto Y is said to be compact (perfect, or proper) if it is closed and point inverses are compact. If h is a continuous function mapping X onto Y then by a compactification of h we mean a pair (X*, h*) where X* is Tychonoff and contains X as a dense subspace, and where h*: X*→Y is a compact extension of h. The idea of a mapping compactification first appeared in (7). In (1) it was shown that any compactification of X determines a compactification of h, and that any compactification of h can be determined in this way. This idea was then developed in (2) and (3).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 19 , Issue 2 , September 1974 , pp. 105 - 108
Copyright
Copyright © Edinburgh Mathematical Society 1974

References

REFERENCES

(1) Cain, G. L. JR., Compactification of Mappings, Proc. Amer. Math. Soc. 23 (1969), 298–303.CrossRefGoogle Scholar
(2) Cain, G. L. JR., Extensions and compactifications of mappings, Math. Ann. 191 (1971), 333–336.CrossRefGoogle Scholar
(3) Cain, G. L. JR., Metrizable Mapping compactifications, General Topology and Appl. 2 (1972), 271–275.CrossRefGoogle Scholar
(4) Firby, P. A., Lattices and compactifications I, Proc. London Math. Soc. (3) 27 (1973), 22–50.CrossRefGoogle Scholar
(5) Firby, P. A., Lattices and compactifications II, Proc. London Math. Soc. (3) 27 (1973), 51–60.CrossRefGoogle Scholar
(6) Njastad, O., A note on compactification by bounding systems, J. London Math. Soc. 40 (1965), 526–532.CrossRefGoogle Scholar
(7) Whyburn, G. T., A unified space for mappings, Trans. Amer. Math. Soc. 74 (1953), 344–350.CrossRefGoogle Scholar