On the Wallman-Frink compactification of 0-dimensional spaces and shape
We construct functors from the shape category (for metrizable spaces) to other categories. These functors allow us to obtain new shape invariants. On the other hand, we give a relation between the Stone-Čech compactification of two metrizable spaces with the same shape. Finally we prove the following result: ``Two metrizable spaces \(X,Y\) such that \(\text{ind}(X)=\text{ind}(Y)=0\) are of the same shape if and only if they are homeomorphic''. This result is a generalization of a theorem due to \textit{G. Kozlowski} and \textit{J. Segal} [Fundam. Math. 83, 151-154 (1974; Zbl 0269.54027)] (in the metrizable case).
Wallman-Frink compactification of a 0-dimensional space
scientific article; zbMATH DE number 62266