itself is called a uniform structure on X. The uniform structure induces a topology on X where the basic neighborhoods of x are sets of the form {y : (x,y)∈U} for U∈Φ. Uniform structure See Uniform space. 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.) Z Zero-dimensional A space is zero-dimensional if it has a base of clopen sets. See also Naive set theory, Axiomatic set theory, and Function for definitions concerning sets and functions. Topology for a brief history and description of the subject area Topological spaces for basic definitions and examples List of general topology topics List of examples in general topology Topology specific concepts Compact space Connected space Continuity Metric space Separated sets Separation axiom Topological space Uniform space Other glossaries Glossary of algebraic topology Glossary of differential geometry and topology Glossary of areas of mathematics Glossary of Riemannian and metric geometry References Also available as Dover reprint. External links A glossary of definitions in topology Topology Wikipedia glossaries using description lists