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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
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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.

Information

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

References

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5. Stone, M. H., Boundedness properties of function lattices, Can. J. Math., 1 (1949), 176–186.Google Scholar