DMS Set Theoretic Topology Seminar

Speaker: Vladimir Tkachuk

Title: Factorization theorem and stability of products of Lindelof Sigma-spaces

Abstract: We will show next that, for any product of Lindelof Sigma-spaces \(X\), if \(f\) is a continuous map of \(X\) onto a space of weight not exceeding \(\kappa\), then this map factorizes continuously  through a face of cardinality \(\kappa\) of \(X\). One of the consequences of this result is a very deep and non-trivial theorem of Arhangel’skii that states that any product of Lindelof Sigma-spaces is stable. We will prove this theorem which is not easy to establish even for the product of real lines.