Finite topology

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It is possible for a topology to be finite in the sense that there are only finitely many open sets. This is an extreme case which has been investigated from a 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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