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 the line segment to the circle. If there was such a map we could remove a point of the line segment and the image of this point on the circle. The remaining pieces would then still be homeomorphic. On the other hand the first one has two components while the second one is still connected. Since connectedness is preserved by bi-continous maps we obtain a contradiction. Therefore a bi-continous map from the line to the circle can not exist. q.e.d.

This Video was produces for a topology seminar at the Leibniz Universitaet Hannover.

http://www-ifm.math.uni-hannover.de/~fugru/?topologie_teil1

Category:

Howto & Style

Tags:

• topology
• mathematics
• homeomorphy
• conectedness
• homeomorphism
• path
• bothmer
• fugru
• cg

[random12331233]

What the watch did i just fuck..and,, at the first place,,How did i get here :o?

[kentoo2020]

cute!