second-countable space
topological space whose topology admits a countable base
topologist's sine curve
connected but not path-connected space; the graph of the function sin(1/𝑥) on the half-open interval (0,1] together with the origin
manifold
topological space that at each point resembles Euclidean space (unspecified type)
topological manifold
topological space (which may also be a separated space) which locally resembles real n-dimensional space
finite topological space
topological space with a finite number of points