Weakly Fréchet–Urysohn and Pytkeev spaces

We study a new pointwise topological property, the weak Fréchet–Urysohn property, introduced by Reznichenko. We also study the property introduced by Pytkeev in 1983. It is proved that sequentiality is strictly stronger than the Pytkeev property, which is strictly stronger than the wFU property, which is strictly stronger than countable tightness. However we prove that a countably tight compact Hausdorff space is Pytkeev. The above properties are used to detect some non-subsequential spaces.