Hausdorff space
topological space in which distinct points have disjoint neighbourhoods
Moore space
developable regular Hausdorff space
Stone space
type of space in topology (branch of mathematics)
locally compact space
topological space such that every point has a neighbourhood with compact closure
Hilbert cube
infinite-dimensional cube with a compact topology
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)
manifold
topological space that at each point resembles Euclidean space (unspecified type)
long line
locally Euclidean topological space that is not paracompact
topological manifold
topological space (which may also be a separated space) which locally resembles real n-dimensional space
manifold with boundary
topological space locally isomorphic to either Euclidean space or to Euclidean half-space
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
barrelled space
Hausdorff topological vector space for which every barrelled set in the space is a neighborhood for 0
Hawaiian earring
one-point compactification of a countably infinite family of open intervals
cellular space
type of Hausdorff space in topology