Quote:
Originally Posted by Ben
Let  be a topological space. Then a neighbourhood of  is any open set containing  . |
Wait a minute, I protest! A neighborhood is not necessarily open!
So long as
has an open subset containing
, it's a neighborhood of it. IOW
musn't belong to the frontier of
, which can however comprise any amount of its frontier and even be fully closed!
Note that this makes it equivalent to define the interior of a set
as being the set of all points of which
is a neighborhood. In topology, so many roads lead to Rome.
----------------
Inutil insegnŕ al mus, si piart timp, in plui si infastiděs la bestie.
Hypography Forum PITA...... er, Administrator.
