show that for any metric space X ,the set X\{x } is open in X.

Question

anonymous · Answer

@JamesJ  pls hlp

jamesj · Answer

So what's the definition of open?d

anonymous · Answer

i think it means division is not applicable on X \{x}

jamesj · Answer

No, not at all.

Look up the definition and when you have it, let me know.

anonymous · Answer

mmm it means that there is a well-defined distance between any two points

jamesj · Answer

No, that's what a metric is.

Don't you have a text book and/or lecture notes? Look it up!

I'm being quite rough with you because metric spaces is an advanced topic that presupposes a high level of intellectual seriousness. I will help you when I see that seriousness.

anonymous · Answer

i understant, i am still new to this module.i  hv 3 days on it.im trying to teach myself

walters · Answer

i think by open they mean  if every point on X has a neighbourhood contained in X

jamesj · Answer

yes. Now using that definition, you need to construct such a neighborhood for every point $ p \in X \backslash  \{ x \} $.