A set 
has compact closure if its set closure is compact.
In a proper metric space, including finite-dimensional
Euclidean space, this is equivalent to 
being bounded.
Compact Closure
See also
Bounded, Compact Set, TopologyThis entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Compact Closure." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompactClosure.html