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On the Local Connectedness of βX-X

Published online by Cambridge University Press:  20 November 2018

R. Grant Woods
R. Grant Woods*
Affiliation:
University of Manitoba, Winnipeg, Manitoba
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Let X be any completely regular Hausdorff topological space, and let βX denote its Stone-Čech compactification. This note is devoted to proving the following result:

5. THEOREM. Let X be realcompact and noncompact. Then βX—X is not connected im kleinen at any point.

Type
Mathematical Notes
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 4 , December 1972 , pp. 591 - 594
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Gillman, L. and Jerison, M., Rings of continuous functions, Van Nostrand, Princeton, N.J., 1960.Google Scholar
2. Henriksen, M. and Isbell, J. R., Local connectedness in the Stone-Čech compactification, Illinois J. Math. 1 (1957), 574-582.Google Scholar
3. Hocking, J. and Young, G., Topology, Addison-Wesley, Reading, Mass., 1961.Google Scholar
4. Woods, R. G., Co-absolutes of remainders of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545-560.Google Scholar