Results 1 to 4 of 4

Math Help - A compact, contented set

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    6
    Awards
    1

    Question A compact, contented set

    Thanks to Laurent's answer to my first post, i was encouraged to resume reading my Edwards, which i had all but given up, due to the many difficult gap-fillers the reader was required to supply. Sure enough, it didn't take long before i've reached another impasse. Consider the attached proof of Proposition 6.1. The last sentence delivers nonchalantly the following opaque claim: "A+ is a compact contented set". Do you understand why this should be so? (Please note that the definition for an "absolutely integrable" function is given on the left leaf)

    P.S.
    The excerpt is taken form C.H. Edwards' "Advanced Calculus of Several Variables", Dover, 1994, which is an unabridged, corrected republication of the work first published by Academic Press, New York, 1973. The book is available for sale in such stores as Amazon and Barnes & Noble (to name a few).
    Attached Thumbnails Attached Thumbnails A compact, contented set-edwards.gif  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by itai View Post
    Consider the attached proof of Proposition 6.1. The last sentence delivers nonchalantly the following opaque claim: "A+ is a compact contented set". Do you understand why this should be so? (Please note that the definition for an "absolutely integrable" function is given on the left leaf)
    I may be mistaking, but isn't it because A^+\subset B^\varepsilon\cup A and both A and B^\varepsilon are compact contented? However, I could'nt find a definition of "compact contented" on the internet so I can't be sure; is it what is usually called "compact"?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2008
    Posts
    6
    Awards
    1

    Some relevant definitions and theorems

    Hi Laurent,

    My reply is in the attached pdf file. Unfortunately, i couldn't get the mathematical symbols to display properly, when i copied the text from the pdf document directly to this message.

    Thanks.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2008
    From
    Paris, France
    Posts
    1,174
    Quote Originally Posted by itai View Post
    Hi Laurent,

    My reply is in the attached pdf file. Unfortunately, i couldn't get the mathematical symbols to display properly, when i copied the text from the pdf document directly to this message.

    Thanks.
    You're right, I gave it too quick a look. And it doesn't seem either correct as such or even simple to correct.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 8th 2012, 10:11 PM
  2. Replies: 1
    Last Post: November 19th 2011, 07:32 AM
  3. Finite union of compact sets is compact
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 8th 2011, 08:43 PM
  4. the intersection of a collection of compact sets is compact
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: February 28th 2010, 02:58 PM
  5. Replies: 2
    Last Post: April 6th 2007, 06:48 PM

Search Tags


/mathhelpforum @mathhelpforum