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Hi, Can ZANyone Explain why is the Stone-Cech Compactification, defined by the space of ultrafilters, is a compact space? —Preceding unsigned comment added by Topologia clalit ( talk • contribs) 07:31, 4 August 2010 (UTC)
Descrete spaces will be helpfull for me too.. Suppose we take the descerete case. I don't understand, Why is the space of ultrafilters defined on X is compact? In the topology we have mentioned a few days ago.. I think that in here it is specified that the space of ultrafilters defined over X is compact Hausdorff for any topological space X: http://en.wikipedia.org/wiki/Stone%E2%80%93%C4%8Cech_compactification Topologia clalit ( talk) 09:57, 4 August 2010 (UTC)
Thanks!!! Topologia clalit ( talk) 10:09, 7 August 2010 (UTC)
What is {Ø}? 199.126.224.156 ( talk) 09:58, 4 August 2010 (UTC)
Since the last programming competition question was answered so quickly, I think I'll try another one that has been bothering me for a long time. I asked before on the computing desk, but the answers didn't really answer the question. This is a paraphrased question from a programming competition I was in many years ago. Note, all numbers are decimal, not integer numbers.
My program was deemed correct, but I know it was wrong because I only tested the situation that the smallest circle goes into the smallest angle corner of the triangle and the largest circle goes into the largest angle corner - leaving the medium circle for the medium angle corner. There is another situation where the circles may be lined up along one side of the triangle, but not fit into the three corners. Is there a simple solution to this problem or is it required to be a complicated task of testing every possible layout for organizing the circles inside the triangle? -- kainaw ™ 12:19, 4 August 2010 (UTC)
I'm presently reading through a set of notes on Vector Calculus and have met a result that I understand but I'm not sure that the notational rules have been observed.
In the term with both an epsilon and a delta, I was under the impression that you're not allowed to let j=k and then sum over j in the delta and simultaneously leave the epsilon, by which the delta is multiplied, unchanged. Is this correct notation? Thanks asyndeton talk 13:40, 4 August 2010 (UTC)
I was thinking about quotient spaces of the sphere. Take the sphere an identify the North and South poles. This can be done many ways; but I have two examples in mind. We can take the poles and pull them away from the centre, pull them around outside of the sphere and then glue them together. This will give a pinched torus (see the left hand image). The other way would be to push the poles into the sphere towards the centre, and then glue them when they meet (see the right hand image). I can see that these are embeddings of the quotient space S2/S0 into R3. I was wondering:
— Fly by Night ( talk) 16:08, 4 August 2010 (UTC)
This raises another question. Denote the pinched torus by P and the object on the right by A. It seems that the interior of P is homeomorphic to the exterior of A and the interior of A is homeomorphic to the exterior of P. Is there a name for this property? Have these kind of objects been studied before? — Fly by Night ( talk) 18:09, 4 August 2010 (UTC)
Mathematics desk | ||
---|---|---|
< August 3 | << Jul | August | Sep >> | August 5 > |
Welcome to the Wikipedia Mathematics Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Hi, Can ZANyone Explain why is the Stone-Cech Compactification, defined by the space of ultrafilters, is a compact space? —Preceding unsigned comment added by Topologia clalit ( talk • contribs) 07:31, 4 August 2010 (UTC)
Descrete spaces will be helpfull for me too.. Suppose we take the descerete case. I don't understand, Why is the space of ultrafilters defined on X is compact? In the topology we have mentioned a few days ago.. I think that in here it is specified that the space of ultrafilters defined over X is compact Hausdorff for any topological space X: http://en.wikipedia.org/wiki/Stone%E2%80%93%C4%8Cech_compactification Topologia clalit ( talk) 09:57, 4 August 2010 (UTC)
Thanks!!! Topologia clalit ( talk) 10:09, 7 August 2010 (UTC)
What is {Ø}? 199.126.224.156 ( talk) 09:58, 4 August 2010 (UTC)
Since the last programming competition question was answered so quickly, I think I'll try another one that has been bothering me for a long time. I asked before on the computing desk, but the answers didn't really answer the question. This is a paraphrased question from a programming competition I was in many years ago. Note, all numbers are decimal, not integer numbers.
My program was deemed correct, but I know it was wrong because I only tested the situation that the smallest circle goes into the smallest angle corner of the triangle and the largest circle goes into the largest angle corner - leaving the medium circle for the medium angle corner. There is another situation where the circles may be lined up along one side of the triangle, but not fit into the three corners. Is there a simple solution to this problem or is it required to be a complicated task of testing every possible layout for organizing the circles inside the triangle? -- kainaw ™ 12:19, 4 August 2010 (UTC)
I'm presently reading through a set of notes on Vector Calculus and have met a result that I understand but I'm not sure that the notational rules have been observed.
In the term with both an epsilon and a delta, I was under the impression that you're not allowed to let j=k and then sum over j in the delta and simultaneously leave the epsilon, by which the delta is multiplied, unchanged. Is this correct notation? Thanks asyndeton talk 13:40, 4 August 2010 (UTC)
I was thinking about quotient spaces of the sphere. Take the sphere an identify the North and South poles. This can be done many ways; but I have two examples in mind. We can take the poles and pull them away from the centre, pull them around outside of the sphere and then glue them together. This will give a pinched torus (see the left hand image). The other way would be to push the poles into the sphere towards the centre, and then glue them when they meet (see the right hand image). I can see that these are embeddings of the quotient space S2/S0 into R3. I was wondering:
— Fly by Night ( talk) 16:08, 4 August 2010 (UTC)
This raises another question. Denote the pinched torus by P and the object on the right by A. It seems that the interior of P is homeomorphic to the exterior of A and the interior of A is homeomorphic to the exterior of P. Is there a name for this property? Have these kind of objects been studied before? — Fly by Night ( talk) 18:09, 4 August 2010 (UTC)