Remainders of normal spaces
The following results are obtained: (1) if \(X\) is locally compact, then \(X\) is the Stone-Čech remainder of a normal space; (2) if \(X\) is first countable and the Stone-Čech remainder of a normal space, then \(X\) is locally compact, (3) if \(X\) is of countable type (\(\equiv\beta X\setminus X\) is a Lindelöf space) then \(X\) is the remainder of a normal space. It is shown that the behaviour of countable spaces which are locally compact except at one point, in context of being normal remainders, is as various as that of arbitrary spaces. It is investigated the property that all normal images are compact.
scientific article; zbMATH DE number 425567