Hostname: page-component-77c89778f8-n9wrp Total loading time: 0 Render date: 2024-07-24T13:20:05.435Z Has data issue: false hasContentIssue false
  • English
  • Français

The k-Extremally Disconnected Spaces as Projectives

Published online by Cambridge University Press:  20 November 2018

Henry B. Cohen
Henry B. Cohen*
Affiliation:
New Mexico State University
Rights & Permissions [Opens in a new window]

Extract

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 letter k denotes an infinite cardinal. A space is a compact Hausdorff space unless otherwise indicated. A space is called extremally disconnected (k-extremally disconnected) if it is the Stone space for a complete (k-complete) Boolean algebra. A map is a continuous function from one space into another. A map f:X —> Y is called minimal if f is onto, but f(M) is properly contained in Y for each closed proper subset M of X. A space F is called free if F has a dense subset X such that every space-valued function on X extends to a map on all of F or, equivalently, if F is the Stone-Cech compactification of some discrete topological space X.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 253 - 260
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Gillman, L. and Jerison, M., Rings of continuous functions (New York, 1960).Google Scholar
2. Gleason, A. M., Projective topological spaces, III. J. Math., 2 (1958), 482–489.Google Scholar
3. Rainwater, John, A note on projective resolutions, Proc. Am. Math. Soc, 10 (1959), 734–735.Google Scholar
4. Sikorsky, R., Boolean algebras (Berlin, 1960).Google Scholar
5. Stone, M. H., Boundedness properties of function lattices, Can. J. Math., 1 (1949), 176–186.Google Scholar