locally convex space
topological vector space in which every vector has a convex neighborhood
webbed space
space where open mapping and closed graph theorems hold
nuclear space
Hausdorff locally convex space such that tensor product with any other Hausdorff locally convex space is uniquely defined (i.e. the projective tensor product is canonically isomorphic to the injective tensor product)
strong operator topology
locally convex topology on function spaces
distinguished space
topological vector space having the property that weak-* bounded subsets of their biduals (i.e. the strong dual space of their strong dual space) are contained in the weak-* closure of some bounded subset of the bidual
Schwartz topological vector space
topological vector space whose neighborhoods of the origin have a property similar to the definition of totally bounded subsets
stereotype space
topological vector space such that the natural map into the second dual space is an isomorphism of topological vector spaces