A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.
Compact Surface
See also
Compact Set, TriangulationThis entry contributed by Todd Rowland
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Rowland, Todd. "Compact Surface." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/CompactSurface.html