I am not well 'accustomed' to these kind of proofs so please bear with my stupidity(adsbygoogle = window.adsbygoogle || []).push({});

Suppose U and V are both open subsets in Rn. Prove that U intersection V and U union V are open as well.

Dfeinition of open is that you cna center a ball about a point a in a set such that that ball is completely contained in the set.

So let there be a ball with center a radius delta in U such that

[tex] B(a,\delta_{1}) = { x: ||x-a||< \delta_{1}} [/tex] for U and

[tex] B(b,\delta_{2}) = { y: ||y-b||< \delta_{2}} [/tex] for V

now the for the union

[tex] B(c, \delta) = {z: ||z-c|| < \delta} [/tex]

and c belongs to the union of U and V. and picking delta = min (delta 1, delta 2) we can say that the ball is completely contained in U union V and the union is open?

If this correct we can move to the intersection...

do i do a similar procedure? Please help?

Thank you for you help and advice!

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# Simple Topology question

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