Compactness and connectedness as composable properties

Abstract

In [5] Magill showed that compactness is a composable property of Hausdorff spaces. (That is, if α,β are compact subsets of X × X, then α ○ β is also compact when X is T2.) Also Magill gave an example to show that the composition of connected relations need not be connected. Subsequently, he characterized Hausdorff k-spaces in terms of the semigroup of compact relations in X.