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Cardinality of discrete subsets of a topological space: Corrigendum

Published online by Cambridge University Press:  17 April 2009

David B. Gauld  and
M.K. Vamanamurthy
David B. Gauld
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
M.K. Vamanamurthy
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag, Auckland, New Zealand.
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Theorem 1 and Corollary 1 of the original paper [Bull. Austral. Math. Soc. 25 (1982), 99–101] are false unless, for example, we assume the Generalised Continuum Hypothesis. The proof of Theorem 1 correctly shows that exp(|c|) ≤ exp(|D|) but one cannot then deduce that the cardinality of C is at most that of D. All one can deduce is that the cardinality of C is less than exp(|D|).

Type
Corrigendum
Information
Bulletin of the Australian Mathematical Society , Volume 29 , Issue 3 , June 1984 , pp. 431
Copyright
Copyright © Australian Mathematical Society 1984