A note on iterated duals of certain topological spaces
A set is called \(\tau\)-saturated if it is the intersection of its neighborhoods; the topology \(\tau^d\) generated by the complements of \(\tau\)-saturated \(\tau\)-compact subsets of \(X\) is called the dual of the topology \(\tau\) on \(X\). It was known that for \(T_1\)-spaces the relation \(\tau^{dd}=\tau^{dddd}\) holds and the author proves as the main result that this relation holds not only for \(T_1\)-topologies. He adds that ``after this paper was accepted, Martin Kovář of the Technical University of Brno communicated to the author a proof that \(\tau^{dd}=\tau^{dddd}\) for all topologies''. However the paper contains some other results on iterated duals, too.
scientific article; zbMATH DE number 1774096