On bisequentiality and spaces of strictly decreasing functions on trees

TL;DR

This paper characterizes spaces of strictly decreasing functions on trees using bisequentiality, addressing open questions and exploring their relation to Corson, Eberlein, and uniform Eberlein compacta.

Contribution

It provides a new characterization of these function spaces in terms of bisequentiality and clarifies their connections to well-known compacta classes.

Findings

Characterization of spaces of decreasing functions via bisequentiality

Answers to open questions from prior work

Relations established between these spaces and classical compacta classes

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.