The concept of essential sequence and essential
space is given within the class of pseudoradial spaces. This
concept tries to clarify the behaviour of convergent (long)
sequences. Various examples and
implications are proved among classes of pseudoradial (and
radial, semiradial, almost radial) essential spaces. It is shown
that essentially radial spaces are the same as pseudoradial
Whyburn spaces. A list of open problems is given.
