
1 Attachment(s)
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 (Speechless)
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) ?

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 cutsoff the given in the question. Do you fear being caught cheating by one of the netsearch programs that check for copying?
http://www.mathhelpforum.com/mathhe...ial19060.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 $

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 cutoff.. has nothing to do with the question.