• December 16th 2011, 12:04 PM
analysis
Let $(R,d)$ be a metric space. Is it true, that for any metric $d$, from $d(x_{n},x)\longrightarrow 0$ follows $d(x_{n}-x,0)$ converges, when $n\longrightarrow\infty$?
Actually, it is not true, but it is terribly difficult to find counterexample
• December 16th 2011, 12:54 PM
girdav
Re: Really difficult about metric space
How is $x_n-x$ defined on a metric space?
• December 16th 2011, 12:58 PM
vincisonfire
Re: Really difficult about metric space
Quote:

Originally Posted by girdav
How is $x_n-x$ defined on a metric space?

I guess you could add what is 0 in your metric space.