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Open sets

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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 sets is again open. The intersection of to open sets is also open. Let X be any set. Every collection T of subsets of X that contains the empty set and X itself and satisfies the two above properties (finite intersections und arbitrary unions stay in T) is called a topoloy on X. A space X with a topology T is called a topological space.This Video was produces for a topology seminar at the Leibniz Universitaet Hannover. http://www-ifm.math.uni-hannov...

Channel: Howto & Style
Uploaded: November 30, 1999 at 12:00 am
Author: bothmer

Length: 00:44
Rating: 4.55
Views: 6262

Tags: bothmer  cg  fugru  intersection  mathematics  open  set  topology  union  

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Video Comments

lazmedina (November 30, 1999 at 12:00 am)
I think that's how babies are formed :)
lazmedina (November 30, 1999 at 12:00 am)
I think that's how babies are formed :)
thefuturebird (November 30, 1999 at 12:00 am)
Intersection of open sets is open. OK got it.
intelite (November 30, 1999 at 12:00 am)
Thank god I am not in hanover u.
nitr0hk (November 30, 1999 at 12:00 am)
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joliteal (November 30, 1999 at 12:00 am)
Por fin alguien explica la genesis de los huesos de melocotón!
bothmer (November 30, 1999 at 12:00 am)
Sure! I clarified the explanation as you suggest.
kstahmer (November 30, 1999 at 12:00 am)
That's an excellent allegory for open sets -- thanks.I believe your remarks need to be changed to finite intersections and arbitrary unions of open sets are open sets.For example, please consider the countable intersection of (-1/n, 1/n) for n = 1, 2, 3, ...Its intersection is { 0 }, which is a closed set.
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