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The Klein Bottle
The Klein Bottle is a surface on which you can move from outside to inside without crossing an edge. This shows that inside and outside...
 
Uploaded: November 8, 2006 at 5:56 pm
Author: bothmer
 
Length: 01:23
Rating: 4.45
Views: 100054
 
Tags: advent  bothmer  bottle  calendar  cg  fugru  geometry  glue  klein  mathematics  moebius  strip  topology  
 
The fundamental Group of the Torus is abelian
This video illustrates the proof of the Theorem in the title. The proof goes like this: Consider a rectangle. Then the path going up the...
 
Uploaded: November 8, 2006 at 6:08 pm
Author: bothmer
 
Length: 01:33
Rating: 4.59
Views: 14882
 
Tags: abelian  bothmer  cg  fugru  fundamental  group  homotopy  math  path  topology  torus  
 
Gluing a Torus
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus.Often...
 
Uploaded: November 8, 2006 at 5:54 pm
Author: bothmer
 
Length: 00:54
Rating: 4.69
Views: 8958
 
Tags: bothmer  cg  fugru  glue  glueing  kampen  mathematics  seifert  topology  torus  van  
 
Compactness and Stereographic Projection
Here the stereographic projection of the sphere to the plane is illustrated. Also a proof that the plane is not compact is shown:Proof: Consider equally...
 
Uploaded: November 8, 2006 at 6:00 pm
Author: bothmer
 
Length: 01:57
Rating: 4.61
Views: 6344
 
Tags: bothmer  cg  compact  fugru  infinity  mathematics  projection  stereographic  topology  
 
Open sets
This video illustrates operations on open sets (symbolized by burning objects). The fire symbolizes that open sets have no border. The union of two open...
 
Uploaded: November 8, 2006 at 6:03 pm
Author: bothmer
 
Length: 00:44
Rating: 4.70
Views: 5498
 
Tags: bothmer  cg  fugru  intersection  mathematics  open  set  topology  union  
 
Not a homeomorphism
Here an operation on a rectangle is shown that is not a homeomorphism. Punching a hole in a topological space is not bi-continuous. After the...
 
Uploaded: November 8, 2006 at 6:01 pm
Author: bothmer
 
Length: 00:39
Rating: 4.33
Views: 1921
 
Tags: bothmer  fire  fugru  homeomorphism  mathematics  topology  
 
Gluing a Sphere
Gluing is a good method to construct new topological spaces from known ones. Here two rectangles are glued to form a sphere.Often the fundamental group...
 
Uploaded: November 8, 2006 at 5:55 pm
Author: bothmer
 
Length: 00:53
Rating: 4.00
Views: 3315
 
Tags: bothmer  cg  fugru  glue  glueing  Kampen  mathematics  Seifert  sphere  topology  van  
 
Null-homotopic Paths
A path is called null homotopic, if it can be contracted to a point.This Video was produces for a topology seminar at the Leibniz Universitaet...
 
Uploaded: November 8, 2006 at 5:57 pm
Author: bothmer
 
Length: 00:49
Rating: 4.00
Views: 1165
 
Tags: bothmer  cg  fugru  homotopy  mathematics  path  topology  
 
Coverings of the Circle
A covering of a topological space X is a topological space Y together with a continuous surjective map from X to Y that is locally...
 
Uploaded: November 8, 2006 at 6:02 pm
Author: bothmer
 
Length: 02:20
Rating: 4.75
Views: 4714
 
Tags: bothmer  cg  circle  covering  fugru  fundamental  group  mathematics  spiral  topology  universal  
 
The fundamental Group
This video illustrated the construction of the fundamental Group of a topological space.Inside a topological space (symbolized by the brown box) we consider paths. Paths...
 
Uploaded: November 8, 2006 at 6:05 pm
Author: bothmer
 
Length: 01:53
Rating: 4.23
Views: 3257
 
Tags: addition  bothmer  cg  element  fugru  fundamental  group  inverse  mathematics  neutral  path  topology  
 


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