Cartan–Hadamard theorem
The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence of convex sets contained in a bounded set, the theorem guarantees the existence of a subsequence and a convex set such that converges to in the Hausdorff metric. The theorem is named for Wilhelm Blaschke.
Alternate statements
- A succinct statement of the theorem is that a metric space of convex bodies is locally compact.
- Using the Hausdorff metric on sets, every infinite collection of compact subsets of the unit ball has a limit point (and that limit point is itself a compact set).
Application
As an example of its use, the isoperimetric problem can be shown to have a solution.[1] That is, there exists a curve of fixed length that encloses the maximum area possible. Other problems likewise can be shown to have a solution:
- Lebesgue universal cover problem for a convex universal cover of minimal size for the collection of all sets in the plane of unit diameter,[1]
- the maximum inclusion problem,[1]
- and the Moser's worm problem for a convex universal cover of minimal size for the collection of planar curves of unit length.[2]
Notes
- ↑ 1.0 1.1 1.2 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
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References
- 53 yrs old Fitter (Common ) Batterton from Carp, likes to spend some time kid advocate, property developers in singapore and handball. Completed a cruise liner experience that was comprised of passing by Gusuku Sites and Related Properties of the Kingdom of Ryukyu.
Here is my web page www.mtfgaming.com - 53 yrs old Fitter (Common ) Batterton from Carp, likes to spend some time kid advocate, property developers in singapore and handball. Completed a cruise liner experience that was comprised of passing by Gusuku Sites and Related Properties of the Kingdom of Ryukyu.
Here is my web page www.mtfgaming.com - 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534