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Math Help - Interior points proof

  1. #1
    Junior Member
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    Red face Interior points proof

    Any hints or clues appreciated.

    Here are my answers so far:

    a) if A ∩ S is emtpy then ∅ ∈ ΩS

    b) Since A ∈ ΩX(which means A is open), there exists r>0 s.t B(x,r) ⊂ U therfore x ∈ intxA.

    c) Don't know

    Suppose x ∈ (intxA) ∩ S....

    d)?
    e)?
    f) U is an open set
    g) All open sets can be expressed as a union of balls
    h) ?
    Attached Thumbnails Attached Thumbnails Interior points proof-123.jpg  
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  2. #2
    MHF Contributor

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    Frankly I am tired of dealing with the way you post questions.
    It is a waste of time on your part as well as our part.
    This current question is unreadable at best.
    Why do you think that any of us ought to know what \Omega S means? What is A~?
    Moreover, you have posted an image that actually cuts-off the given in the question. Do you fear being caught cheating by one of the net-search programs that check for copying?

    http://www.mathhelpforum.com/math-he...ial-19060.html
    Why not learn to post in symbols? You can use LaTeX tags
    Here is an example.
    [tex]\Omega S[tex] gives \Omega S
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  3. #3
    Junior Member
    Joined
    May 2010
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    Sorry thought that this notation was standard...
    ΩX = The set af all open sets in X
    ΩS = The set af all open sets in S

    These are tutorial questions, not any assignment questions(we only write tests), so cheating not an issue, there are no marks invovled... The top part which is cut-off.. has nothing to do with the question.
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