A filter on a collection of finite sets and Eberlein compacta

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.