DMS Set Theoretic Topology Seminar

Speaker: Rongxin Shen

Abstract. This is joint work with Heikki Junnila. The notion of a reflexive family of sets in topological spaces originated in research on the invariant subspace problem in functional analysis. In [Fund. Math., 192 (2006), 111--120], Yang and Zhao introduced the s-reflexive spaces in which reflexive families can be characterized in a simple way. We prove that every s-reflexive Hausdorff space is zero-dimensional, and we indicate a close relationship between the theory of s-reflexive spaces and that of continuous selections. Several examples relating to s-reflexivity are given. Also we will talk about some unsolved problems on this topic.