nLab
coherent topological space
**
topology**
algebraic topology
## Basic concepts
*
space
*
locale
*
topological space
*
continuous map
*
homeomorphism
*
Top
*
nice topological space
*
nice category of spaces
*
convenient category of topological spaces
* **
homotopy theory**
*
homotopy group
*
covering space
## Theorems
*
Whitehead's theorem
*
Freudenthal suspension theorem
*
nerve theorem
## Extra stuff, structure, properties
*
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
*
manifold
## Examples
*
point,
real line,
plane
*
sphere,
ball,
annulus
*
polytope,
polyhedron
*
loop space,
path space
*
Cantor space,
Sierpinski space
*
long line,
Warsaw circle
A topological space $X$ is coherent if
This is equivalent to saying that the topos of sheaves $Sh(X)$ on $X$ is a coherent topos.
Revised on May 26, 2010 13:31:54
by
Mike Shulman
(75.3.130.212)