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diameter (Definition)

Let $A$ a subset of a pseudometric space $(X,d)$ . The diameter of $A$ is defined to be $$\sup\{d(x,y) : x\in A, y\in A\}$$ whenever the supremum exists. If the supremum doesn't exist, diameter of $A$ is defined to be infinite.

Having finite diameter is not a topological invariant.




"diameter" is owned by drini. [ owner history (1) ]
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See Also: pi

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Cross-references: topological invariant, finite, infinite, supremum, pseudometric space, subset
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This is version 1 of diameter, born on 2002-02-15.
Object id is 1989, canonical name is Diameter.
Accessed 3282 times total.

Classification:
AMS MSC54-00 (General topology :: General reference works )

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