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Special morphisms for zero-set spaces

Published online by Cambridge University Press:  17 April 2009

Christopher R.A. Gilmour
Christopher R.A. Gilmour
Affiliation:
Department of Mathematics, University of Cape Town, Rondebosch, Republic of South Africa.
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Abstract

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The author obtains characterizations of the quotients, epimorphisms and extreme monomorphisms in the category of separated zero-set spaces and zero-set maps (defined by Hugh Gordon [Pacific J. Math. 36 (1971), 133–157]). The method employed, that of initiality constructions, is also used to elucidate the relationship between zero-set spaces and certain other topological structures by means of forgetful functors and their right inverses. Characterizations of pseudocompactness for zero-set spaces then follow.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 13 , Issue 1 , August 1975 , pp. 57 - 68
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Alexandroff, A.D., “Additive set-functions in abstract spaces”, Rec. Math. [Mat. Sbornik] N.S. 8 (50) (1940), 307–348.Google Scholar
[2]Alexandroff, A.D., “Additive set-functions in abstract spaces”, Rec. Math. [Mat. Sbornik] N.S. 9 (51) (1941), 563–628.Google Scholar
[3]Alexandroff, A.D., “Additive set-functions in abstract spaces”, Rec. Math. [Mat. Sbornik] N.S. 13 (55) (1943), 169–238.Google Scholar
[4]Antoine, Philippe, “Étude élémentaire des catégories d'ensembles structurés”, Bull. Soc. Math. Belg. 18 (1966), 142–164.Google Scholar
[5]Brümmer, Guillaume C.L., “A categorial study of initiality in uniform topology”, (PhD thesis, University of Cape Town, Cape Town, 1971).Google Scholar
[6]Canfell, M.J., “Dimension theory in zero-set spaces”, Pacific J. Math. 47 (1973), 393–400.CrossRefGoogle Scholar
[7]Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (Van Nostrand, Princeton, New Jersey; Toronto; London; New York; 1960).CrossRefGoogle Scholar
[8]Gilmour, Christopher R.A., “Zero-set spaces and pseudocompactness”, (MSc thesis, University of Cape Town, Cape Town, 1974).Google Scholar
[9]Gordon, Hugh, “Rings of functions determined by zero-sets”, Pacific J. Math. 36 (1971), 133–157.Google Scholar
[10]Hager, Anthony W., “Measurable uniform spaces”, Fund. Math. 77 (1972), 51–73.CrossRefGoogle Scholar
[11]Hager, Anthony W., “Some nearly fine uniform spaces”, Proc. London Math. Soc. (3) 28 (1974), 517–546.CrossRefGoogle Scholar
[12]Hager, Anthony W., “Vector lattices of uniformly continuous functions and some categorical methods in uniform spaces”, TOPO 72 -General topology and ite applications, 172–187 (Lecture Notes in Mathematics, 378. Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar
[13]Hager, Anthony W., “Uniformities induced by proximity, cozero and Baire sets”, Trans. Amer. Math. Soc. (to appear).Google Scholar
[14]Herrlich, Horst, Topologische Reflexionen und Coreflexionen (Lecture Notes in Mathematics, 78. Springer-Verlag, Berlin, Heidelberg, New York, 1968).CrossRefGoogle Scholar
[15]Salbany, S., “Realcompactness of zero-set spaces”, Math. Colloq. Univ. Cape Town 9 (1974), 17–18.Google Scholar
[16]Speed, T.P., “On rings of sets II. Zero-sets”, J. Austral. Math. Soc. 16 (1973), 185–199.CrossRefGoogle Scholar
[17]Tashjian, Gloria, “Cozero and Baire maps on products of uniform spaces”, Preprint.Google Scholar