Is the set D={(x,y)∈R²:x²+y²<1} complete?
how?
actually i am in dark how to do it.
thanks in advance
There is a common theorem which says that for subspaces of a complete space completeness and closedness are synonomous. To be more explicit, if $\displaystyle D$ were complete the sequence $\displaystyle \displaystyle 1-\frac{1}{n}$ (I'm thinking in $\displaystyle a+bi$ notation) would converge to some point of $\displaystyle D$. Does it?