A set has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that is bounded.
Compact Closure
See also
Bounded, Compact Set, TopologyThis entry contributed by Todd Rowland
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Rowland, Todd. "Compact Closure." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CompactClosure.html