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.
Essentially Pseudoradial Spaces
SORANZO, Alessandro;TIRONI, GINO
2012-01-01
Abstract
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.File in questo prodotto:
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