Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-12-01T04:47:21.100Z Has data issue: false hasContentIssue false
  • English
  • Français

On Subspaces of Replete and Measure Replete Spaces

Published online by Cambridge University Press:  20 November 2018

Peter Grassi
Peter Grassi*
Affiliation:
Hofstra University HempsteadN.Y. 11550
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.

The concepts of repleteness and more generally measure repleteness are investigated for set-theoretic lattices on specific subspaces of a lattice space. These general results are then applied to specific topological spaces, and we obtain as special cases some known theorems as well as some new results concerning for example, ∝-completeness, realcompactness, measure compactness and Borel-measure compactness.

Keywords

28A60
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 58 - 64
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Alexandroff, A. D., Additive set functions in abstract spaces, Mat. Sb. (N.S.) (9) 51 (1941), 563-628.Google Scholar
2. Bachman, G. and Sultan, A., Regular lattice measures; mappings and spaces, Pacific J. Math. 67 (1976), 291-321.Google Scholar
3. Bachman, G. and Sultan, A., On regular extensions of measures, Pacific J. Math. (2) 86 (1980), 389-395.Google Scholar
4. Bachman, G. and Sultan, A., Measure theoretic techniques in topology and mappings of replete and measure replete spaces, Bull. Austral. Math. Soc. (2) 18 (1978), 267-285.Google Scholar
5. Dykes, N., Generalizations of realcompact spaces, Pacific J. Math. 33 (1970), 571-581.Google Scholar
6. Frolik, Z., A generalization of realcompact spaces, Czech. Math. J. (13) 88 (1963), 127-137.Google Scholar
7. Gardner, R. J., The regularity of Borel measures and Borel-measure compactness, Proc. Lon. Math. Soc. (3) 30 (1975), 95-113.Google Scholar
8. Halmos, P., Measure Theory (Van Nostrand, New York; 1950).Google Scholar
9. Hoffman-Jorgensen, J., The theory of analytic spaces (Various Publications Series, 10. Matematisk Institut, Aarhus Universitet, Aarhus, Denmark, 1970).Google Scholar
10. Kirk, R. B., Measures in topological spaces and B-compactness, K. Nederl. Akad. Wetensch., Proc. Ser. A 72; Indag. Math. 31 (1969), 172-183.Google Scholar
11. Moran, W., Measures and mappings on topological spaces, Proc. Lon. Math. Soc. 19 (1969), 493-508.Google Scholar
12. Mrόwka, S., Some properties of Q-spaces, Bull. Acad. Polan. Sci. Ser. Sci. Math. Astronom. Phys. 5 (1957), 947-950.Google Scholar
13. Szeto, M., Measure repleteness and mapping preservations, J. Ind. Math. Soc. 43 (1979), 35-52.Google Scholar
14. Varadarajan, V. S., Measures on topological spaces, Amer. Math. Soc. Transi. Ser. 2, 48 (1965), 161-228.Google Scholar
15. Wallman, H., Lattices and topological spaces, Ann. of Math. 39 (1938), 112-126.Google Scholar
16. Wenjen, C., Realcompact spaces, Port. Math. 25 (1966), 135-139.Google Scholar