Sets with the Baire property in topologies formed from a given topology and ideals of sets. (English) Zbl 1378.54002
Two topologies \(\mathcal{T_1}\) and \(\mathcal{T_2}\) on the same set \(X\) are \(\pi\)-compatible if for each nonempty element \(U\) of \(\mathcal{T_1}\) there is a nonempty element \(V\) of \(\mathcal{T_2}\) which is a subset of \(U\) and vice versa. Some properties of \(\pi\)-compatible topologies are investigated.
Reviewer: Jan Borsik (Kosice)
MSC:
| 54A10 | Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) |
