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.