 trustle > EngliSea > M > math > Luffa Glome in colors
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/i.php?f=5253#5309 Hollow Glome and Luffa
A hollow glome can be a counterexample to the Poincaré conjecture. It is simply connected, closed 3-manifold but is not homeomorphic to the 3-sphere or glome.
http://qindex.info/i.php?f=5253#3558 3-sphere
Any loop or circular path on the 3-sphere can be continuously shrunk to a point without leaving the 3-sphere. The Poincaré conjecture provides that the 3-sphere is the only three-dimensional manifold (up to homeomorphism) with these properties.
http://qindex.info/i.php?f=5253#3447

Cartesian product
For sets A and B, the Cartesian product A × B is the set of all ordered pairs(a, b) where a ∈ A and b ∈ B.
http://qindex.info/i.php?f=5253#3619

Closed set
A set which contains all its limit points. A closed set contains its own boundary.
http://qindex.info/i.php?f=5253#3476

Compact space
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/i.php?f=5253#3494

Connected space
A topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. Otherwise, X is said to be connected.
http://qindex.info/i.php?f=5253#3492

Contractible space
In mathematics, a topological space X is contractible if the identity map on X is null-homotopic, i.e. if it is homotopic to some constant map.
http://qindex.info/i.php?f=5253#3578 How Fast Is It - 02 - The Speed of Light
How Fast Is It - 02 - The Speed of Light (1080p)
http://qindex.info/i.php?f=5253#5359 How Fast Is It - 03 - Special Relativity
How Fast Is It - 03 - Special Relativity (1080p)
http://qindex.info/i.php?f=5253#5358 How Fast Is It - 04 - General Relativity I - Geometry
How Fast Is It - 04 - General Relativity I - Geometry (1080p)
http://qindex.info/i.php?f=5253#5355 How the Universe Works
Blow your Mind of the Universe Part 11 - Space Discovery Documentary
http://qindex.info/i.php?f=5253#5380

Implicit Function
2018-12-02 08:49
http://qindex.info/i.php?f=5253#3572

Implicit function theorem
2018-12-02 09:00
http://qindex.info/i.php?f=5253#3651 Leonard Susskind
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/i.php?f=5253#5242 Loop
A loop in mathematics, in a topological space X is a continuous function f from the unit interval I = [0,1] to X such that f(0) = f(1).
http://qindex.info/i.php?f=5253#3450 n-ball
A set of points whose distance from a particular point is less than a specified length in n-dimensional space.
http://qindex.info/i.php?f=5253#3445 n-sphere
A set of points at a specified distance from a particular point in (n+1)-dimensional space. The pair of points at the ends of a line segment is a 0-sphere.
http://qindex.info/i.php?f=5253#3446 Path
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 path-connected.
http://qindex.info/i.php?f=5253#3453

Poincaré conjecture
Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere.
http://qindex.info/i.php?f=5253#3579

Real coordinate space
In mathematics, real coordinate space of n dimensions, written Rn (/ɑːrˈɛn/ ar-EN) (also written ℝn with blackboard bold) is a coordinate space that allows several (n) real variables to be treated as a single variable.
http://qindex.info/i.php?f=5253#3495

Simply connected space
A topological space X is called simply connected if it is path-connected and any loop in X defined by f : S1 → X can be contracted to a point.
http://qindex.info/i.php?f=5253#3534

Simply connected space
A sphere (or, equivalently, a rubber ball with a hollow center) is simply connected, because any loop on the surface of a sphere can contract to a point, even though it has a "hole" in the hollow center.
http://qindex.info/i.php?f=5253#3577 Singularities Explained | Infinite Series
Singularities Explained | Infinite Series
http://qindex.info/i.php?f=5253#3563 Space
A space consists of selected mathematical objects that are treated as points, and selected relationships between these points.
http://qindex.info/i.php?f=5253#5251 The Poincare Conjecture
In the early 1900s mathematicians and physicists were very interested in the shape of space. New experiments and theories were being developed that would ultimately create relativity theory and change our entire view of the universe.
http://qindex.info/i.php?f=5253#3533 Thinking visually about higher dimensions
Thinking visually about higher dimensions
http://qindex.info/i.php?f=5253#3388

Three-torus
The three-dimensional torus, or triple torus, is defined as the Cartesian product of three circles. The triple torus is a three-dimensional compact manifold with no boundary.
http://qindex.info/i.php?f=5253#3612 Tom Campbell
The assumption that space and time is continuous yields Zeno's paradox. The universe is not created out of continuous space and time.
http://qindex.info/i.php?f=5253#5024

Topological manifold
A topological space which locally resembles real n-dimensional space in a sense defined below.
http://qindex.info/i.php?f=5253#3493 volumes and surface areas of n-spheres
Graphs of volumes and surface areas of n-spheres of radius 1.
http://qindex.info/i.php?f=5253#3448 Zeno's Paradox
To get to a point in the geometric space, you have to travel half way to that point and half way to that halfway point and so on. There's no end to the halfway so you can't reach the point.
http://qindex.info/i.php?f=5253#5248 -  