Countably compact weakly Whyburn spaces (Q1677511)

The author discusses the properties of weakly Whyburn spaces, and proves that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and shows that the Urysohn assumption is essential by constructing a countably compact Hausdorff non-weakly Whyburn space of cardinality \(\omega_1\). The author also considers the question under which conditions every weakly Whyburn space is pseudoradial. The following results are proved: (1)\, there is a countably compact regular weakly Whyburn non-pseudoradial space; (2)\, a space \(X\) is pseudoradial if it is an initially \(\kappa\)-compact weakly Whyburn regular space with \(\chi(X)\leq\kappa^+\); (3)\, a space \(X\) is pseudoradial if it is a regular weakly Whyburn \(P\)-space of countable extent with \(\chi(X)\leq\omega_2\).