Approaching Openness in R^2: Investigating Open Balls

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I typed the question and my attempt at a solution below...

euclidmetric.png


It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.
 
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jdinatale said:
I typed the question and my attempt at a solution below...

euclidmetric.png


It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.

If it's open, its complement is closed. What happens if you sneak up to it from above? Or below?
 

Thread 'Finding the nth roots of a complex number'

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