- #1

ssayan3

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## Homework Statement

T is open relative to X iff for any p [tex]\in[/tex] S there exists [tex]\delta[/tex] > 0 such that B(p,[tex]\delta[/tex] )[tex]\cap[/tex]X is [tex]\subset[/tex] T

## Homework Equations

T is open relative to X provided there exists an open subset U of R^n such that T = U[tex]\cap[/tex]X

## The Attempt at a Solution

Okay, so, going the forward ("if") direction, I think I'm able to classify this problem into one of three major subsets: X is closed, open, or neither. So, dealing with X being closed, I so far have:

1. Pick p in T

2. By hypothesis, produce U, an open subset of R^n s.t. T = U[tex]\cap[/tex]X

3. For all points qn in U, let tau= min{|qn - p|}

4.

...

I believe that the final step will involve producing a delta ball within T, but I dn't know how to go about finding the correct delta. As well, if what I have so far is correct, then I think i'll have to end up letting delta be the minimum of tau and some other variable that I'll call beta for right now; so, how do I find the right beta?

Does anyone have any ideas for the reverse ("only if") direction?

Thanks guys!

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