On a problem by A. Hajnal and I. Juhász (Q1029940)

\textit{A. Hajnal} and \textit{I. Juhász} asked in [Problems (p. 637), Topics in topology. Colloquia Mathematica Societatis Janos Bolyai. 8. Amsterdam-London: North-Holland Publishing Company. 643 p. (1974; Zbl 0278.00018)] whether \(\lambda^\omega=\lambda\) whenever \(\lambda\) is the cardinality of a Hausdorff topology on an infinite set. The authors describe an example with the claim that the cardinality of its topology is \(\aleph_\omega (<\aleph_\omega^{\;\omega})\). Unfortunately the topology has cellularity \(\aleph_\omega\) and hence cardinality \(2^{\aleph_\omega}\).