A metric space $\displaystyle X$ is said to be locally compact if every point of $\displaystyle X$ has a compact neighborhood. Show that a compact metric space $\displaystyle X$ is locally compact.
A metric space $\displaystyle X$ is said to be locally compact if every point of $\displaystyle X$ has a compact neighborhood. Show that a compact metric space $\displaystyle X$ is locally compact.
Regards,
Raed.
X is a neighborhood of each and every point in it, so...