A note on rank 2 diagonals

Abstract

We solve two questions regarding spaces with a ($G_{\hat{I}}´$)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos regarding weakly Lindelöf spaces with a $G_{\hat{I}}´$-diagonal of rank 2 and the other is a question of Arhangel'skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.