# Finite topology

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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 of surfaces. A surface is said to have finite topology if it is homeomorphic to a compact 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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