Coarser connected topologies
This paper investigates topological spaces which have coarser connected topologies. If in a collectionwise normal space \(X\), the density equals the extent, which is attained and at least \(c\), then \(X\) has a coarser connected collectionwise normal topology. The authors point out that the separation property collectionwise normal can be replaced by other separation properties. A zero-dimensional metrizable space \(X\) of density at least \(c\) has a coarser connected metrizable topology. A non-\(H\)-closed Hausdorff space with a \(\sigma\)-locally finite base has a coarser connected Hausdorff topology. The authors give necessary and sufficient conditions for an ordinal to have a coarser connected Urysohn topology. In addition, the authors present a nowhere locally compact Hausdorff space \(X\) with no coarser connected Hausdorff topology, yet \(X\) is dense in a connected Hausdorff space \(Y\).
scientific article; zbMATH DE number 2117950