The algebraic properties of the morphological operators are important but they are not alone in this. Topological properties can be equally important and are explored in depth in this chapter. The basic elements of topology are summarized, followed by those of metric spaces, notably the Hausdorff metric. Compact sets are then defined and this leads to the hit-or-miss topology and the myope topology. Semi-continuity is explained and a proposition concerning basis representation is advanced.

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Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Heijmans, H.J.A.M. (2020). Hit-or-miss topology and semi-continuity. In Advances in Imaging and Electron Physics (pp. 217–251). doi:10.1016/bs.aiep.2020.07.007