Categorical Properties
The main interest in approach spaces and their contractions is that they form a category with good properties, while still being quantitative like metric spaces. One can take arbitrary products and coproducts and quotients, and the results appropriately generalize the corresponding results for topologies. One can even "distancize" such badly non-metrizable spaces like βN, the Stone–Čech compactification of the integers.
Certain hyperspaces, measure spaces, and probabilistic metric spaces turn out to be naturally endowed with a distance. Applications have also been made to approximation theory.
Read more about this topic: Approach Space
Famous quotes containing the words categorical and/or properties:
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—Leontine Young (20th century)
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—Ralph Waldo Emerson (1803–1882)