I am trying to learn complete metric space, & in some lecture video (on youtube) I found the definition of complete metric space that it is a set with no holes. I do understand the concept of cauchy sequence & complete metric space given in Kolmogorov's analysis but I can't find an example of a set with no holes.

Question

anonymous · Answer

@KingGeorge please help me whenever you are online

anonymous · Answer

@2:38 http://www.youtube.com/watch?v=kjpPakKMJqQ

kinggeorge · Answer

Well, the easiest set to see that has no holes (for me) is the real numbers. Any sequence contained within the real numbers will always converge in the reals. Another easy set to see is closed is the complex set. It's basically the same thing as the reals.

If you're looking for sets with holes, a simple way would be to just remove a point from a set with no holes. 

I hope this helps.

anonymous · Answer

thanks a tonne

anonymous · Answer

@KingGeorge one more question are the concepts such as contact point, closure, limit point, isolated point etc for metric space are similar to the topology?

kinggeorge · Answer

I'm not entirely sure about that second question, but I would assume the answer is yes.