Definition of Subbasis. Meaning of Subbasis. Synonyms of Subbasis

- In topology, a subbase (or subbasis, prebase, prebasis) for the topology τ of a topological space (X, τ) is a subcollection B {\displaystyle B} of τ {\displaystyle...
- is the su****t relation and not the subset relation). A neighbourhood subbasis at x {\displaystyle x} is a family S {\displaystyle {\mathcal {S}}} of...
- filter on a set has the finite intersection property. Every neighbourhood subbasis at a point in a topological space has the FIP, and the same is true of...
- { P ∈ X F : a ∈ P } {\displaystyle H(a)=\{P\in X_{F}:a\in P\}} form a subbasis for the Harrison topology. The product is a Boolean space (compact, Hausdorff...
- there is a subbasis such that every open cover of the topological space from elements of the subbasis has a subcover with at most two subbasis elements...
- define a vector topology it suffices to define a neighborhood basis (or subbasis) for it at the origin. Theorem (Neighborhood filter of the origin)—Suppose...
- extension topology on X {\displaystyle X} is the topology having as a subbasis the union of τ and the family of all subsets of X {\displaystyle X} whose...
- Homeomorphism Local homeomorphism Open and closed maps Embedding Germ Basis Subbasis Open cover Locally finite space Covering space Atlas Limit point Net Filter...
- {P}}} and r {\displaystyle r} ranges over the positive real numbers is a subbasis at the origin for the topology induced by P {\displaystyle {\mathcal {P}}}...
- clopen down-sets of X. (d) Clopen up-sets and clopen down-sets of X form a subbasis for (X,τ). (e) For each pair of closed subsets F and G of X, if ↑F ∩ ↓G...