A note on rank 2 diagonals

Abstract

We solve two questions regarding spaces with a (Gδ)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos regarding weakly Lindel\"of spaces with a Gδ-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.

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