Lets do it this way


lets start with open sets on the real line


Given some point a, lets call $\{x : |x-a| < d\}$ where $d>0$


the open ball around a


Ill write it this way $B_d(a)$


to mean the open ball around a of radius d


Note that this is just the interval (a-d,a+d)


its the interval centered at a having a total length d


Lets define open sets for this case:


@usukidoll are you with me so far?

It's a hyperbola and then I can't tell ... I got the boundary points
wouldn't the interior point be at the center which is (0,0) meep

complex analysis and real analysis b4 topology ;p

boundary as in there are points inside that set and points outside that set

it's like...
we have closed if the points are outside of S. It's an exterior point.

but it seems like the hyperbola is never ending. it doesn't stop :/
'

but it's like the original equation is
x^2-y^2=4
so I assumed that we are taking the parts that are going outwards

don't know
directions
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this is the original problem

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this is what I graphed
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so the http://prntscr.com/i3ppq0
boundary points is only (-pi,0) and (0,pi)
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I think we can put a circle in between these intervals.. the center (0,0)