Question

Select the Bounded set from the given
options.​

Answer 1

Answer:

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Answer 2

Answer:

Geometrically, the diameter of a closed globe in En could be defined as the maximum distance between two of its points. In an open globe in En, there is no "maximum" distance (why?), but we still may consider the supremum of all distances inside the globe. Moreover, this makes sense in any set A⊆(S,ρ). Thus we accept it as a general definition, for any such set.

Definition

The diameter of a set A≠∅ in a metric space (S,ρ), denoted dA, is the supremum (in E∗ ) of all distances ρ(x,y), with x,y∈A;1 in symbols,

dA=supx,y∈Aρ(x,y).(3.9.1)

If A=∅, we put dA=0. If dA<+∞,A is said to be bounded ( in (S,ρ)).