- Fσ set
- An Fσ set is a countable union of closed sets.
- Filter
- A filter on a space X is a nonempty family F of subsets of X such that the following conditions hold:
- The empty set is not in F.
- The intersection of any finite number of elements of F is again in F.
- If A is in F and if B contains A, then B is in F.
- Finer topology
- If X is a set, and if T1 and T2 are topologies on X, then T2 is finer (or larger, stronger) than T1 if T2 contains T1. Beware, some authors, especially analysts, use the term weaker.
- Finitely generated
- See Alexandrov topology.
- First category
- See Meagre.
- First-countable
- A space is first-countable if every point has a countable local base.
- Fréchet
- See T1.
- Frontier
- See Boundary.
- Full set
- A compact subset K of the complex plane is called full if its complement is connected. For example, the closed unit disk is full, while the unit circle is not.
- Functionally separated
- Two sets A and B in a space X are functionally separated if there is a continuous map f: X → such that f(A) = 0 and f(B) = 1.
Read more about this topic: Glossary Of Topology