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The Klein Bottle

Click To Watch	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: 4.48 Views: 109520   Tags: advent  bothmer  bottle  calendar  cg  fugru  geometry  glue  klein  mathematics  moebius  strip  topology

The fundamental Group of the Torus is abelian

Click To Watch	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: 4.62 Views: 15618   Tags: abelian  bothmer  cg  fugru  fundamental  group  homotopy  math  path  topology  torus

Gluing a Torus

Click To Watch	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: 4.71 Views: 9541   Tags: bothmer  cg  fugru  glue  glueing  kampen  mathematics  seifert  topology  torus  van

Compactness and Stereographic Projection

Click To Watch	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: 4.63 Views: 6591   Tags: bothmer  cg  compact  fugru  infinity  mathematics  projection  stereographic  topology

Open sets

Click To Watch	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: 4.55 Views: 5701   Tags: bothmer  cg  fugru  intersection  mathematics  open  set  topology  union

Not a homeomorphism

Click To Watch	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: 2043   Tags: bothmer  fire  fugru  homeomorphism  mathematics  topology

Gluing a Sphere

Click To Watch	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: 3561   Tags: bothmer  cg  fugru  glue  glueing  Kampen  mathematics  Seifert  sphere  topology  van

Null-homotopic Paths

Click To Watch	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: 1212   Tags: bothmer  cg  fugru  homotopy  mathematics  path  topology

Coverings of the Circle

Click To Watch	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: 4.77 Views: 4884   Tags: bothmer  cg  circle  covering  fugru  fundamental  group  mathematics  spiral  topology  universal

The fundamental Group

Click To Watch	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: 4.29 Views: 3434   Tags: addition  bothmer  cg  element  fugru  fundamental  group  inverse  mathematics  neutral  path  topology

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