nice topological space
nice category of spaces
convenient category of topological spaces
Freudenthal suspension theorem
CW-complex, Hausdorff space, second-countable space, sober space
compact space, paracompact space
connected space, locally connected space, contractible space, locally contractible space
topological vector space, Banach space, Hilbert space
point, real line, plane
sphere, ball, annulus
loop space, path space
Cantor space, Sierpinski space
long line, Warsaw circle
Edit this sidebar
For S⊂X a subset of a topological space X, a, interior point of S is a point x∈S which has a neighbourhood in X that is contained in S. The union of all interior points is the interior S ∘ of S.
In general, we have S ∘⊆S. S is open if and only if S ∘=S.
Compare the topological closure S¯ and frontier ∂S=S¯∖S ∘.