Hey guys, I have a problem from my Topology course that I can't seem to figure out. Any help would be appreciated. Here it is:
The distance functions D'=D/(1+D) and D''= min{D,1} are each metrics on M. Let x M and let R>0.
Let:
S '(x)={y M|D'(x,y)< }
S ''(x)={y M|D''(x,y)< }
a) Prove that S ''(x) S '(x).
b)Prove that S '(x) S ''(x).
It almost seems to me like the containment should be switched in part a at least, but I don't know.
Thanks in Advance.