W
- Weak topology
- The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous.
- Weaker topology
- See Coarser topology. Beware, some authors, especially analysts, use the term stronger topology.
- Weakly countably compact
- A space is weakly countably compact (or limit point compact) if every infinite subset has a limit point.
- Weakly hereditary
- A property of spaces is said to be weakly hereditary if whenever a space has that property, then so does every closed subspace of it. For example, compactness and the Lindelöf property are both weakly hereditary properties, although neither is hereditary.
- Weight
- The weight of a space X is the smallest cardinal number κ such that X has a base of cardinal κ. (Note that such a cardinal number exists, because the entire topology forms a base, and because the class of cardinal numbers is well-ordered.)
- Well-connected
- See Ultra-connected. (Some authors use this term strictly for ultra-connected compact spaces.)
Read more about this topic: Glossary Of Topology