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
adjoint functor theorem
adjoint lifting theorem
small object argument
Freyd-Mitchell embedding theorem
relation between type theory and category theory
sheaf and topos theory
enriched category theory
higher category theory
A topological groupoid X 1→t→sX 0 is called proper if the continuous map
(s,t):X_1 \to X_0\times X_0
is a proper map.
In particular the automorphism group of any object in a proper topological groupoid is a compact group. In this sense proper topological groupoids generalize compact groups.
A Lie groupoid is called a proper Lie groupoid if its underlying topological groupoid is proper.
An orbifold is a proper Lie groupoid which is also an étale groupoid.