Products of Michael spaces and completely metrizable spaces (Q2701655)

The Michael space \(M(A,C)\), for \(A\cup B\subset [0,1], A\cap B=\emptyset\), is the set \(A\cup B\) where the points of \(C\) are isolated and the points of \(A\) inherit neighborhoods from [0,1]. Let \(B(\kappa)\) denote a countable power of a discrete space of cardinality \(\kappa\). Main results: 2.2. There is a Lindelöf \(M(A,C)\) of weight \(\omega_1\) such that \(M(A,C)\times B(\omega)\) is Lindelöf and \(M(A,C)\times B(\omega_1)\) is not normal; 3.3. If \(M(A,[0,1]\smallsetminus A)\times B(\omega)\) is normal then \(M(A,[0,1]\smallsetminus A)\times S\) is normal for every completely metrizable \(S\); 4.4. [Fleissner axiom] If \(M(A,C)\times B(\omega_1)\) is normal then \(M(A,C)\times S\) is normal for every completely metrizable \(S\) (not true in ZFC).