Question about open extensions of sets in metric spaces.
Let be an arbitrary metric space. For every and , we define the open -extension of as the set
It seems intuitive that, given and , we should have that . However, I haven't been able to even begin to construct a rigorous argument to prove it. Any hint or proposed direction would be greatly appreciated (or counterexample in the event that it is false).
Re: Question about open extensions of sets in metric spaces.
When you say that you are unable "to construct a rigorous argument", does that mean that you cannot even start?
Originally Posted by RaisinBread
Can you show that
Before I work on this, please post what you have been able to do.