
Glome in colors
 R
What is the shape of the universe?
Does it extend infinitely?
We can go around the earth forever but can not find the end. Likewise, the universe may be finite and endless.
Let's consider a mathematical model suitable for such a space.
http://qindex.info/d.php?c=5253#5309


3sphere
 R
Any loop or circular path on the 3sphere can be continuously shrunk to a point without leaving the 3sphere. The Poincaré conjecture provides that the 3sphere is the only threedimensional manifold (up to homeomorphism) with these properties.
http://qindex.info/d.php?c=5253#3447


Basic Euclidian Geometry
 R
By stringing an infinite number of lines along a dimension perpendicular to the line, a twodimensional object called a plane can be obtained. And then if we string an infinite number of planes in either direction, we get three dimensional space.
http://qindex.info/d.php?c=5253#5249

Compact space
 R
Compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded(that is, having all its points lie within some fixed distance of each other).
http://qindex.info/d.php?c=5253#3494


Leonard Susskind
 R
The space itself may be more than three dimensions. But we can't visualize more dimensions. The architecture of the brain itself is evolved in the world of three dimensions. We only describe more dimensions by pure mathematics.
http://qindex.info/d.php?c=5253#5242


Path
 R
In mathematics, a path in a topological space X is a continuous function f from the unit interval I = [0,1] to X
f : I → X.
A topological space for which there exists a path connecting any two points is said to be pathconnected.
http://qindex.info/d.php?c=5253#3453

