Coreflectors not preserving the interval and Baire partitions of uniform spaces

Tashjian, G.; Vilímovský, J.

doi:10.1090/S0002-9939-1979-0542094-8

Coreflectors not preserving the interval and Baire partitions of uniform spaces
HTML articles powered by AMS MathViewer

by G. Tashjian and J. Vilímovský PDF

Proc. Amer. Math. Soc. 77 (1979), 257-263 Request permission

Abstract:

Values of the compact interval and other spaces under coreflectors in the category of uniform spaces are studied. It is shown that any coreflector which changes the usual uniformity of the interval produces a new uniformity which contains all finite Baire partitions of the interval.

References

Zdeněk Frolík, Four functors into paved spaces, Seminar Uniform Spaces (Prague, 1973–1974) Mat. Ustav Československé Akad. Věd, Prague, 1975, pp. 27–72. MR 0440511
Zdeněk Frolík, Measurable uniform spaces, Pacific J. Math. 55 (1974), 93–105. MR 383358
A. W. Hager, Three classes of uniform spaces, General topology and its relations to modern analysis and algebra, III (Proc. Third Prague Topological Sympos., 1971) Academia, Prague, 1972, pp. 159–164. MR 0353270
J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
J. F. Kennison, Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303–315. MR 174611, DOI 10.1090/S0002-9947-1965-0174611-9
M. D. Rice and G. J. Tashjian, Cartesian-closed coreflective subcategories of uniform spaces, Trans. Amer. Math. Soc. 276 (1983), no. 1, 289–300. MR 684509, DOI 10.1090/S0002-9947-1983-0684509-6
Jiří Vilímovský, Generation of coreflections in categories, Comment. Math. Univ. Carolinae 14 (1973), 305–323. MR 375211