On bisequentiality and spaces of strictly decreasing functions on trees

Abstract

We present a characterization of spaces of strictly decreasing functions on trees in terms of bisequentiality. This characterization answers Questions 6.1 and 6.2 of "A filter on a collection of finite sets and Eberlein compacta" by T. Cie\'sla. Moreover we study the relation between these spaces and the classes of Corson, Eberlein and uniform Eberlein compacta.