Compact spaces and the pseudoradial property, I

We investigate two properties and their connection to the property of pseudoradiality in the context of compact spaces. The first is the WAP property introduced by P. Simon and the second is the ℵ0-pseudoradial property introduced by B. Shapirovskiı̆. We show that ♢ implies there is a compact space which is pseudoradial but not WAP. We show that there is a model in which CH fails and in which all compact spaces of weight at most ℵ2 are ℵ0-pseudoradial.