Homeomorphic Type
The following three pieces of information completely determine the homeomorphic type of a surface (Massey 1996):
1. Orientability,
2. Number of boundary components,
See also
Algebraic Topology, Euler Characteristic
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References
Massey, W. S. Algebraic Topology: An Introduction. New York: Springer-Verlag, 1996.
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Cite this as:
Weisstein, Eric W. "Homeomorphic Type." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HomeomorphicType.html