Topology Fact
@TopologyFact
Followers
74K
Following
22
Media
279
Statuses
6K
Tweets on topology and geometry from @JohnDCook.
Joined January 2010
"I want to start a new field of geometry where two things are equivalent if you can stretch one into the other without tearing.". "I've got just what you need: a collection of sets closed under finite intersections and arbitrary unions.". "Huh?!".
8
35
333
Counterpart of the Pythagorean theorem for a sphere
johndcook.com
The Pythagorean theorem does not hold on a sphere like the Earth, though it approximately holds if the triangle is small.
0
0
6
A Lindelöf space is a topological space in which every open cover has a countable subcover.
3
8
132
The sum of the squares over the edges of any n-dimensional box is equal to the sum of the squares over the diagonals.
2
9
62
You can form a regular n-simplex by taking the convex hull of the unit basis vectors in R^n+1.
5
11
80
DONUT: Database of Original & Non-Theoretical Uses of Topology .
0
2
14
A Polish space is a separable completely metrizable topological space.
11
10
180
The kth homotopy group of a sphere S^d is trivial if k < d.
3
7
93
There are three regular solids in dimensions 5 and higher: regular simplex, hypercube, and cross polytope.
2
5
26
π-Base: a database of topological examples
topology.pi-base.org
A community database of topological theorems and spaces, with powerful search and automated proof deduction.
0
2
9
R^n has a unique differential structure unless n = 4. R^4 has infinitely many differential structures.
16
50
501
The tangent bundle of a Lie group G is always trivial, i.e. G × R^n.
1
10
118
RT @SamuelGWalters: The Poincaré-Hopf Theorem states that the Euler characteristic of a compact smooth manifold can be found using the degr….
0
18
0