Let (E,d) be a metric space.
Show that the function d'(x,y) = d(x,y)/1 + (d(x,y)) is a metric on E topologically equivalent to d.
Is it metrically equivalent to d'?
Let (E,d) be a metric space.
Show that the function d'(x,y) = d(x,y)/1 + (d(x,y)) is a metric on E topologically equivalent to d.
Is it metrically equivalent to d'?
Thanks
Perhaps I'm just in a caustic mood this morning, but how can you possibly be studying topology and write
"d(x, y)/1 + d(x, y)" to mean $\displaystyle \frac{d(x, y)}{1 + d(x, y)}$??