Bulletin of the Australian Mathematical Society: Volume 29 -

Cardinality of discrete subsets of a topological space: Corrigendum
David B. Gauld, M.K. Vamanamurthy
Published online by Cambridge University Press:

17 April 2009, p. 431
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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|).

Bulletin of the Australian Mathematical Society