? 2022 Elsevier B.V.For a space X, let e(X)=ω?sup{|D|:D is a closed discrete subset in X}, which is called the extent of X. A space is almost discrete if it has at most one non-isolated point. A main theorem here is to prove the following: If ZFC is consistent, then it is consistent with and independent of ZFC that there are a monotonically normal space X and an almost discrete space Y such that X×Y is normal and e(X×Y)>e(X)?e(Y)=ω. Before reaching this, we prove several related results in ZFC.
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