I would like to recieve a hint on how to get started with a proof on
$M \subset X$ and $(M,d)$ is complete then $M$ is closed
I highly believe that there are alot of proofs regarding the above, but I'm afraid that if I google it I will be exposed to a solution, and I only want a hint, so that I can get started. ¨
This is the information I have been given:
What a metric space is.
Def. of convergent seq. in metric space.
Def. of Cauchy seq. in metric space.
A metric space $(X,d)$ is called complete if every Cachy seq. is convergent.
If $d'$ is a metric equivalent to $d$ then $(X,d)$ is complete iff $(X,d')$ is complete.
What an open ball is.
An closed set is the complement of an open set.
What an open set is.