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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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 01:23
Rating: 4.52
Views: 135876
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 01:33
Rating: 4.63
Views: 17433
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:54
Rating: 4.73
Views: 10929
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 01:57
Rating: 4.65
Views: 7225
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:44
Rating: 4.55
Views: 6285
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:39
Rating: 4.33
Views: 2293
 
Tags: bothmer  fire  fugru  homeomorphism  mathematics  topology  
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:49
Rating: 4.00
Views: 1316
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 02:20
Rating: 4.77
Views: 5198
 
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 30, 1999 at 12:00 am
Author: bothmer
 
Length: 01:53
Rating: 4.13
Views: 3905
 
Tags: addition  bothmer  cg  element  fugru  fundamental  group  inverse  mathematics  neutral  path  topology  
 
Non-homeomorphic Topological Spaces
This clip shows two non homeomorphic topological spaces (a line segment and a circle). Proof: We have to show that there is no bi-continuos map from...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:24
Rating: 5.00
Views: 2005
 
Tags: bothmer  cg  conectedness  fugru  homeomorphism  homeomorphy  mathematics  path  topology  
 


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