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diameter (Definition)

Let $A$ a subset of a pseudometric space $(X,d)$. The diameter of $A$ is defined to be

\begin{displaymath}\sup\{d(x,y) : x\in A, y\in A\}\end{displaymath}

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
There are 8 references to this entry.

This is version 1 of diameter, born on 2002-02-15.
Object id is 1989, canonical name is Diameter.
Accessed 2756 times total.

Classification:
AMS MSC: 54-00 (General topology :: General reference works )
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