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First Countable Lindelöf Extensions of Uncountable Discrete Spaces

Published online by Cambridge University Press:  20 November 2018

Murray Bell  and
John Ginsburg
Murray Bell
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T2N2
John Ginsburg
Affiliation:
University of Winnipeg, Winnipeg, Manitoba, Canada.
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The existence of a first countable Lindelöf extension L of an uncountable discrete space D for which L-D is countable is considered. Assuming CH, such extensions exist; however it is also consistent that no such spaces exist, as follows from MA + ¬ CH

Keywords

5402054A25First countableLindelöfdiscreteCH and B(ω)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 23 , Issue 4 , 01 December 1980 , pp. 397 - 399
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Alster, K. and Zenor, P., An example concerning the preservation of the Lindelôf property in product spaces, in Set-Theoretic Topology, éd. G. M. Reed, Academic Press 1977.Google Scholar
2. Kunen, K., Combinatorics, in Handbook of Mathematical Logic, ed. J. Barwise, North- Holland, Amsterdam 1977.Google Scholar
3. Rudin, M. E., Lectures on set-theoretic topology, CBMS series, No. 23, AMS 1975.Google Scholar