Closure-preserving covers and \(\sigma\)-products (Q1101990)

In 1959 Corson obtained the following result: If X is the \(\sigma\)- product of separable metric spaces \(X_ t\), \(t\in T\), then X is Lindelöf. The authors present some generalization of the Corson theorem: If X is the \(\sigma\)-product of Lindelöf spaces \(X_ t\), \(t\in T\), where each \(X_ t\) has a closure-preserving cover by compact sets, then X is Lindelöf. Some special kinds of the notion of closure- preserving, which are preserved by products, are studied.