Thread: how to prove a closed set in Rⁿ

hi!

what is the easiest way to prove that the set A is closed and the set B is not closed?

1). A={(x,y) ∈ R²: x²+y²=1}
and
2). B={(x,y) : ∈ R²: x² - y²=1}



Help please. thanks please

Originally Posted by sorv1986

hi!

what is the easiest way to prove that the set A is closed and the set B is not closed?

1). A={(x,y) ∈ R²: x²+y²=1}
and
2). B={(x,y) : ∈ R²: x² - y²=1}



Help please. thanks please

I mean, the easiest way would be to note that , is continuous (it's just a polynomial) and and for the second one are you sure it isn't closed?

oho....actually the 2nd one i think its a hyperbola...so it should be not closed...am i wrong?.....but in the first case...i did not understand what r u actually doing to prove that set A is closed