Spaces of continuous functions in elementary generic extensions (Q1095438)

We prove some statements on the nonpreservation of cardinal invariants under multiplication of spaces of the form \(C_ p(X)\). By \(C_ p(X)\) we mean the space of all continuous real-valued functions on X with the topology of pointwise convergence. In particular, \(C_ p(X)\) is a topological group. Theorem: The addition of a single Cohen or random real gives rise in the extended model of two Lindelöf spaces \(Y_ 0\) and \(Y_ 1\) with a single nonisolated point each such that \(C_ p(Y_ 0)\) and \(C_ p(Y_ 1)\) are Lindelöf spaces but their procuct is not a Lindelöf space.