Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T05:15:06.425Z Has data issue: false hasContentIssue false
  • English
  • Français

Natural Covers and R-Quotient Maps

Published online by Cambridge University Press:  20 November 2018

S. M. Karnik  and
S. Willard
S. M. Karnik
Affiliation:
Department of Mathematics, University of Alberta, Edmonton Alberta Canada
S. Willard
Affiliation:
Department of Mathematics, University of Alberta, Edmonton Alberta Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We extend the comprehensive treatment of k-spaces and sequential spaces provided by Franklin's refined notion of a natural cover to kR-spaces and sR-spaces. For this purpose, an apparently unstudied class of maps of topological spaces, the class of R-quotient maps, is introduced.

Keywords

54A1054C9954D5054D55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 4 , 01 December 1982 , pp. 456 - 461
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Arens, R., A topology of spaces of transformations, Ann. of Math. 47 (1946), 480-495.Google Scholar
2. Arhangel'skii, A., Some types of factor mapping and the relations between classes of topological spaces, Dokl. Akad. Nauk SSSR 153 (1963), 743-746 [ = Sov. Math. Dokl. 4 (1963), 1726-1729].Google Scholar
3. Arhangel'skii, A., Bicompact sets and the topology of spaces, Trudy Moskov. Mat. Obsc. 13 (1965), 3-55 O Trans. Moscow Math. Soc. (1965), 1-62].Google Scholar
4. Arhangel'skii, A., A characterization of very k-spaces, Czechoslovak Math. J. 18 (93) (1968), 392-395.Google Scholar
5. Franklin, S. P., Spaces in which sequences suffice, Fund. Math. 57 (1965), 107-115.Google Scholar
6. Arhangel'skii, A., Natural covers, Comp. Math. 21 (1969), 253-261.Google Scholar
7. Juhasz, I., Cardinal functions in topology, Math. Centre Tract 34, Math. Centrum Amsterdam, 1971.Google Scholar
8. Mazur, S., On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229-238.Google Scholar
9. Michael, E., A note on k-spaces and kR-spaces, Topology Conference, Arizona State Univ., 1967, 247-249.Google Scholar
10. Noble, N., The continuity of functions on Cartesian products, Trans. Amer. Math. Soc. 149 (1970), 187-198.Google Scholar
11. Schedler, D. A., On topologies determined by clustering sequences: A generalization of sequential spaces, Doct. Dissert., George Washington Univ., 1971.Google Scholar
12. Tanaka, Y., On quasi-k spaces, Proc. Japan Acad. 46 (1970), 1074-1079.Google Scholar
13. Whyburn, C. T., Compactness of certain mappings, Amer. J. Math. 81 (1959), 306-314.Google Scholar