- Finite topology
It is possible for a
topologyto 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 homeomorphicto a compactsurface 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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