I came across this text in Rudin's book where it has been mentioned that a non-empty finite set is closed.
But a closed set is a set which contains all of it's limit points in the set itself but none of the elements of a non-empty finite set can possibly have a limit point because a neighborhood of a limit point has infinite points . So how come a non-empty finite set be a closed set ??
Best Answer
Disregarding possible fine print of definitions the resolution is quite simple:
If there are no limit points, then of course all limit points are trivially contained in the set.