Show that for any metric space X , the set X \ {x} is open in X .i know that an open set in X is an open ball but i don't really get it
Show that for any metric space X , the set X \ {x} is open in X .i know that an open set in X is an open ball but i don't really get it
Unfortunately, what you "know" isn't true. In a metric space, every open ball is an open set, but the other way is not true- not every open set is an open ball.Show that for any metric space X , the set X \ {x} is open in X .i know that an open set in X is an open ball but i don't really get it