Borel–Carathéodory theorem: Difference between revisions

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In [[functional analysis]] and related areas of [[mathematics]] a '''Montel space''', named after [[Paul Montel]], is any [[topological vector space]] in which an analog of [[Montel's theorem]] holds.  Specifically, a Montel space is a [[barrelled space|barrelled]] [[topological vector space]] where every [[closed set|closed]] and [[bounded set (topological vector space)|bounded set]] is [[compact space|compact]].  That is, it satisfies the [[Heine–Borel property]].
== 'interstellar warships to limit my martial arts headquarters ==


In classical [[complex analysis]], Montel's theorem asserts that the space of [[holomorphic function]]s on an [[open set|open]] [[connected space|connected]] subset of the [[complex number]]s has this property.
Observation corridors. And now it has entered the flood a chamber which,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_42.htm オークリー スポーツサングラス], Luo Feng follow to enter.<br><br>secret room that only a large display,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_5.htm オークリー 野球用サングラス].<br><br>'This is a damaged starship.' flood plain face,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_38.htm ゴルフ サングラス オークリー], 'when I found it,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_48.htm ロードバイク サングラス オークリー], it has been damaged and can no longer fly into the universe,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_20.htm オークリー サングラス 通販], but ...... even if it is an empty shell of interstellar warships, defense degree far more than any other base on Earth Municipal Building. '<br><br>'Then I have the ability, I will get it out of the ground.'<br><br>'interstellar warships to limit my martial arts headquarters! Even laser cannon,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_73.htm オークリー ゴルフ サングラス], can never expect to break interstellar warships.' Hung point display screen suddenly lights up the sky picture emerges of the universe. 'This is not our universe ...... Many ordinary people believe the Earth is so simple.'<br><br>'Our Earth humans sometimes very arrogant,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_73.htm オークリー ゴルフ サングラス].'<br><br>'even a variety of animals on land,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_12.htm オークリー サングラス 人気], plant species and many never noticed. ocean
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<ul>
 
  <li>[http://hnwzbl.com/plus/feedback.php?aid=396 http://hnwzbl.com/plus/feedback.php?aid=396]</li>
 
  <li>[http://waw.funbbs.me/viewthread.php?tid=19142&extra= http://waw.funbbs.me/viewthread.php?tid=19142&extra=]</li>
 
  <li>[http://cloud.d1xy.com/forum.php?mod=viewthread&tid=254326 http://cloud.d1xy.com/forum.php?mod=viewthread&tid=254326]</li>
 
</ul>


Many Montel spaces of contemporary interest arise as spaces of [[test function]]s for a space of [[distribution (mathematics)|distributions]]. The space C<sup>∞</sup>(&Omega;) of [[smooth function]]s on an open set &Omega; in '''R'''<sup>''n''</sup> is a Montel space equipped with the topology induced by the family of [[seminorm]]s
== so it fills. ==
:<math>\|f\|_{K,n} = \sup_{|\alpha|\le n}\sup_{x\in K}\left|\partial^\alpha f(x)\right|</math>
for ''n''&nbsp;=&nbsp;1,2,… and ''K'' ranges over compact subsets of &Omega;, and &alpha; is a [[multi-index]].  Similarly, is the space of [[compact support|compactly supported]] functions in an open set with the [[final topology]] of the family of inclusions <math>\scriptstyle{C^\infty_0(K)\subset C^\infty_0(\Omega)}</math> as ''K'' ranges over all compact subsets of &Omega;.  The [[Schwartz space]] is also a Montel space.


No infinite-dimensional [[Banach space]] is a Montel space, since these cannot satisfy the Heine–Borel property: the closed unit ball is closed and bounded, but not compact.
'There is momentum,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_42.htm オークリー サングラス 激安], how to build it?' Hung also eyes shine.<br><br>three brothers from the earth,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_32.htm オークリー 自転車 サングラス], as if like a country boy, amazed looking at a tall building! This is a building of 'cosmic galaxy bank' tall, built a three-dimensional effect is completely rivers like the stars come out.<br><br>looked as if the face of the building ,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_28.htm オークリーレーダーサングラス]...... blowing sky.<br><br>'Qiu Lone Star last time I went in once, you can see again, still very shocked.'<br><br>'Look, the door to this bank,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_77.htm オークリーサングラス画像], the momentum is not the same.' Raytheon stick pouting, indicating the distance.<br><br>Luo Feng looked,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_38.htm オークリー サングラス ファストジャケット].<br><br>Indeed,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_13.htm オークリー サングラス ゴルフ], occasionally to the universe galaxy banks who stare between the momentum is clearly not normal! After all ...... here is the minimum deposit Black Dragon 100 million dollars,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_22.htm オークリー サングラス 種類], the richest man in the ordinary one planet,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_31.htm オークリーサングラス ランキング], so it fills.<br><br>'go, we go.' Luo Feng said.<br><br>'ah.' Hung, Raytheon also full of expectations.<br><br>three and
 
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They have the following properties:
<ul>
* The strong dual of a Montel spaces is Montel.
 
* Montel spaces are reflexive
  <li>[http://www.tecnologo.org.br/home/cadastroempresa/many-members-see-my-eyes-are-wrong-luo-feng-whispered http://www.tecnologo.org.br/home/cadastroempresa/many-members-see-my-eyes-are-wrong-luo-feng-whispered]</li>
* A [[nuclear space|nuclear]] quasi-complete [[barrelled space]] is Montel.
 
* [[Frechet space|Frechet]] Montel spaces are separable and have a [[bornological space|bornological]] strong dual.
  <li>[http://www.zwj521.com/viewthread.php?tid=204549&extra= http://www.zwj521.com/viewthread.php?tid=204549&extra=]</li>
 
 
==References==
  <li>[http://bbs.zcfangw.com/showtopic-1277017.aspx http://bbs.zcfangw.com/showtopic-1277017.aspx]</li>
* {{springer|title=Montel space|id=p/m064880}}
 
* {{cite book |last=Robertson |first=A.P. |coauthors= W.J. Robertson |title= Topological vector spaces |series=Cambridge Tracts in Mathematics |volume=53 |year=1964 |publisher= [[Cambridge University Press]] | page=74}}
</ul>
* {{cite book | last = Schaefer | first = Helmuth H. | year = 1971 | title = Topological vector spaces  | series=[[Graduate Texts in Mathematics|GTM]] | volume=3  | publisher = Springer-Verlag | location = New York | isbn = 0-387-98726-6 | page=147 }}
* {{cite book|first=François|last=Treves|title=Topological Vector Spaces, Distributions and Kernels|publisher=Dover|year=2006|isbn=978-0-486-45352-1}}.
 
{{Functional Analysis}}
 
[[Category:Topological vector spaces]]
 
 
{{Mathanalysis-stub}}

Latest revision as of 17:39, 24 February 2014

'interstellar warships to limit my martial arts headquarters

Observation corridors. And now it has entered the flood a chamber which,オークリー スポーツサングラス, Luo Feng follow to enter.

secret room that only a large display,オークリー 野球用サングラス.

'This is a damaged starship.' flood plain face,ゴルフ サングラス オークリー, 'when I found it,ロードバイク サングラス オークリー, it has been damaged and can no longer fly into the universe,オークリー サングラス 通販, but ...... even if it is an empty shell of interstellar warships, defense degree far more than any other base on Earth Municipal Building. '

'Then I have the ability, I will get it out of the ground.'

'interstellar warships to limit my martial arts headquarters! Even laser cannon,オークリー ゴルフ サングラス, can never expect to break interstellar warships.' Hung point display screen suddenly lights up the sky picture emerges of the universe. 'This is not our universe ...... Many ordinary people believe the Earth is so simple.'

'Our Earth humans sometimes very arrogant,オークリー ゴルフ サングラス.'

'even a variety of animals on land,オークリー サングラス 人気, plant species and many never noticed. ocean 相关的主题文章：

so it fills.

'There is momentum,オークリー サングラス 激安, how to build it?' Hung also eyes shine.

three brothers from the earth,オークリー 自転車 サングラス, as if like a country boy, amazed looking at a tall building! This is a building of 'cosmic galaxy bank' tall, built a three-dimensional effect is completely rivers like the stars come out.

looked as if the face of the building ,オークリーレーダーサングラス...... blowing sky.

'Qiu Lone Star last time I went in once, you can see again, still very shocked.'

'Look, the door to this bank,オークリーサングラス画像, the momentum is not the same.' Raytheon stick pouting, indicating the distance.

Luo Feng looked,オークリー サングラス ファストジャケット.

Indeed,オークリー サングラス ゴルフ, occasionally to the universe galaxy banks who stare between the momentum is clearly not normal! After all ...... here is the minimum deposit Black Dragon 100 million dollars,オークリー サングラス 種類, the richest man in the ordinary one planet,オークリーサングラス ランキング, so it fills.

'go, we go.' Luo Feng said.

'ah.' Hung, Raytheon also full of expectations.

three and 相关的主题文章：

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