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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: 4.747086
Views: 563767
 
Tags: advent  calendar  geometry  topology  mathematics  moebius  strip  klein  bottle  glue  bothmer  fugru  cg  
 
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...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:53
Rating: 4.5333333
Views: 9611
 
Tags: topology  mathematics  glueing  glue  sphere  Seifert  van  Kampen  bothmer  fugru  cg  
 
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....
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:54
Rating: 4.591837
Views: 37145
 
Tags: topology  mathematics  glueing  glue  torus  seifert  van  kampen  bothmer  fugru  cg  
 
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: 4.3809524
Views: 12615
 
Tags: topology  mathematics  open  set  union  intersection  bothmer  fugru  cg  
 
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: 4.756098
Views: 43494
 
Tags: topology  math  fundamental  group  torus  abelian  path  homotopy  bothmer  fugru  cg  
 
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...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:49
Rating: 4.25
Views: 4008
 
Tags: topology  mathematics  homotopy  path  bothmer  fugru  cg  
 
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...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 01:57
Rating: 4.40625
Views: 16500
 
Tags: topology  mathematics  compact  stereographic  projection  infinity  bothmer  fugru  cg  
 
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...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:24
Rating: 5.0
Views: 4923
 
Tags: topology  mathematics  homeomorphy  conectedness  homeomorphism  path  bothmer  fugru  cg  
 
Not null-homotopic Paths
Paths are null-homotopic if they can be contracted to a point. The path in the clip is not null-homotopic, since it can not wiggle past...
 
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer
 
Length: 00:18
Rating: 4.75
Views: 3025
 
Tags: topology  mathematics  homotopy  path  bothmer  fugru  cg  
 
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: 4.857143
Views: 12233
 
Tags: topology  mathematics  universal  covering  circle  spiral  fundamental  group  bothmer  fugru  cg  
 


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