I'm quite new to topology. Just wondering if anyone can help me out a bit.
Let Show is an open subset of
We want to show that there exists an such that .
Suppose that .
Thus, if we add those inequalities, we have
Then, choose for .
Hence, must be open.
Is the above working correct?
Is using the infinity distance function instead of the euclidean distance function, mathematically correct? Could I have used something like instead?
Is there anyway to simplify the working out? What is the best way choosing an epsilon?
Thanks in advance.