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In [[mathematics]], an [[open cover]] of a [[topological space]] <math>X</math> is a set of open subsets such that <math>X</math> is the union of all of the open sets. In [[algebraic topology]], an open cover is called a '''good cover''' if all open sets and all multiple intersections, <math> U_{\alpha_1 \ldots \alpha_n} = U_{\alpha_1 \ldots \alpha_{n-1}} \cap U_{\alpha_n}</math>, are contractible.{{Citation needed|date=June 2011}}
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The concept was introduced by Bott and Tu on [[differential manifold]]s, demanding the <math>U_{\alpha_1 \ldots \alpha_n}</math> to be [[diffeomorphic]] to the <math>n</math>-dimensional [[Euclidean space]] <math>\mathbb{R}^n</math>.
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==Application==
A major reason for the notion of a good cover is that the [[Leray spectral sequence]] of a [[fiber bundle]] degenerates for a good cover, and so the [[Čech cohomology]] associated to a good cover is the same as the Čech cohomology of the space. (Such a cover is known as a [[Leray cover]].)
 
==Example==
 
To cover the two sphere <math> S^2 </math> with a good cover one needs at least 4 open sets.
 
==References==
 
*{{cite book | last = Bott | first = Raoul | authorlink = Raoul Bott | coauthors = Loring Tu | title = Differential Forms in Algebraic Topology | year = 1982 | publisher = Springer | location = New York | isbn = 0-387-90613-4}} &sect;5, S. 42
 
[[Category:Algebraic topology]]
[[Category:Cohomology theories]]
[[Category:Homology theory]]

Revision as of 07:23, 3 March 2014

The island of Tenerife is the largest of the Canary Islands, and probably the most favored by readers. Actually, studies claim that throughout the last one hundred years travelers have increased from one hundred a year to a staggering 11 million. For an island of only 778,000 inhabitants...

Have you ever discovered Tenerife yet? Several UK travelers explain as their dream holiday island Tenerife. So, what"s it concerning this area helping to make it so well-liked by the UK visitors?

The island of Tenerife is the greatest of the Canary Islands, and the absolute most favored by visitors. Actually, studies claim that during the last one hundred years travelers have increased from one hundred per year to a staggering 11 million. For an island of only 778,000 people, this is a remarkable level of tourism and suggests that Tenerife actually has quite a bit to create home about!

So why do so many people come here? Unsurprisingly it would seem that the British come for sunlight. An instant peak at the average temperature in summer and in winter, which usually only varies by about 10 degrees, will concur that Tenerife is the perfect destination for all those fed up with the British climate. Even in the height of summer, Tenerife usually has a westerly wind which helps to keep it at a moderate temperature.

Although Tenerife is most likely best-known for the southern beaches and golf resorts, the island is obviously among marked contrasts from golden sands to black volcanic beaches; from mountain peaks to green valleys. It"s this extraordinary landscape which not just draws in those wanting to enjoy the warm beaches but also attracts those wanting a more effective, walking o-r nature-based holiday. Logo contains further about when to do this activity.

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