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Thread: 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 $\displaystyle \Omega S$ means? What is $\displaystyle A~?$
    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 $\displaystyle \Omega S $
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  3. #3
    Junior Member
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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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