A filter on a collection of finite sets and Eberlein compacta

TL;DR

The paper introduces a new $\sigma$-ideal and filter to demonstrate that a specific space is a non-bisequential Eberlein compactum, advancing understanding of compact space structures.

Contribution

It presents novel $\sigma$-ideal and filter constructions to analyze Eberlein compacta, providing new insights into their topological properties.

Findings

Established a new $\sigma$-ideal on $\omega_1 imes \omega_1$

Constructed a filter on graphs of decreasing partial functions

Proved the space is a non-bisequential Eberlein compactum

Abstract

We introduce a $\sigma$-ideal on $\omega_1 \times \omega_1$ and a filter on the collection of graphs of strictly decreasing partial functions on $\omega_1$ taking values in $\omega_1$. We use them to prove that a certain space is a non-bisequential Eberlein compactum.