- Finite topology
It is possible for a

topology to be finite in the sense that there are onlyfinitely many open sets. This is an extreme case which has been investigated froma combinatorial point of view.The term

**finite topology**is also encountered in a completely different sense in the study ofsurfaces . A surface is said to have finite topology if it ishomeomorphic to acompact surface with finitely many points removed. There may be further variations on this definition according to the category in which one is working.

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