Pseudoradial vs strongly pseudoradial (Q517131)

A space \(X\) is strongly pseudoradial if for any non-closed \(A\subset X\) there is a limit ordinal \(\gamma\) and continuous \(f:\gamma+1\to X\) such that \(f(\gamma)\subset A\) and \(f(\infty_\gamma)\notin A\), where \(\gamma+1=\gamma\cup\{\infty_\gamma\}\). Links between this property and related properties are considered: for example a strongly pseudoradial space is essentially pseudoradial, almost radial and weakly Whyburn but the converse fails. The product of a compact pseudoradial (resp. weakly Whyburn) space and a strongly pseudoradial space is pseudoradial (resp. weakly Whyburn) while the product of finitely many compact strongly pseudoradial spaces is strongly pseudoradial.