Tychonoff expansions in which a given set is open
Let \((X,\tau)\) be a Tikhonov space without isolated points. There is a finer Tikhonov topology \(\tau'\) without isolated points containing a given dense-in-itself set \(A\) such that \(\tau'|A=\tau|A\) if and only if \(A\) does not intersect the closure of the set of isolated points of \(X\setminus A\). The possibility to find a Tikhonov dense-in-itself expansion \(\tau'\) of \(\tau\) that satisfies just \(A\in\tau'\) (or just \(\text{int}_{\tau'} A=\text{int}_{\tau} A\) instead) is also characterized.
scientific article; zbMATH DE number 1955989
scientific article