is a type of mathematical space
is a type of metric space that is bounded
is a metric space (𝑋,𝑑) where the distance (𝑑) between any two points is at most some constant 𝛼
- thus any subset of 𝑋 is a bounded set

Bounded Metric Spaces - Examples

[0,1]³ “unit cube” is a bounded metric space
[0,1]^𝑛 of any finite dimension is a bounded metric space
[0,1]^∞ of infinite dimension is a bounded metric space (but not totally bounded)

Bounded Metric Spaces - Non-Examples