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Which books can I study (learn) better the topics about convergence in $\Bbb R^{n}$ and euclidean space ? Please can you give me an advice some book names? Thank you!

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Convergence is always coordinatewise. –  Berci Mar 23 '13 at 20:57
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What? I just want to learn a book name about these @berci –  B11b Mar 23 '13 at 20:59
    
@B11: This should probably be Community Wiki. Do you have any objections to making it CW? –  robjohn Mar 25 '13 at 19:23
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3 Answers

up vote 4 down vote accepted

See chapter 16 of Mathematical Analysis II by V. A. Zorich. A Universitext colection of Springer Edition. A wonderful book.

Cover of the book written by V. A. Zorich

This chapter and the chapter beyond are dedicated to Uniform Convergence and Basic Operations of Analysis.

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Thank you for suggestion –  B11b Mar 25 '13 at 17:11
    
No need for such a large image! –  lhf Mar 25 '13 at 17:22
    
There is an image of the cover on the linked page. Is it beneficial to include an image (much less, such a large image) here? –  robjohn Mar 25 '13 at 19:35
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Try Analysis in Euclidean Space by Hoffman, reissued by Dover.

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Hmm this is good book. I looked at this. Well, what else? –  B11b Mar 23 '13 at 21:27
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I reviewed this book for the MAA-I think it's the best one there is for this particular aspect of convergence. –  Mathemagician1234 Mar 25 '13 at 17:09
    
The MAA review is available at mathdl.maa.org/mathDL/19/…. –  lhf Mar 25 '13 at 17:13
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Espaces Vectoriels Normés et Topologie:Rédigé par Yannick Privat.

Topologie pour la Licence: Cours et exercices Clemens Berger1

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