On the other hand, she consists of infinitely many separate sets with distinct neighborhoods, so you be the judge.
Imma let you finish, but Hausdorff and the guy who decided to draw sets as balls have the best topology joke of all time.
Acquire one dirty mind, and look at the depiction on the right
no, dear. it does not make you look fat :)
Nah, the best sets-as-balls joke OF ALL TIME is on page 82 of Lang's Algebra (3rd ed.)
Whew! We found a new space to enter!
Your Momma's so fat that she has only interior points.
your momma's so dense her closure is all of R^3
Your momma is so fat her closure consists of interior points only.
(your argument would include (-1/n,1/n), and thats not what we want^^)
Hmm. Agree that my suggestion was faulty. OTOH there are sets of measure zero with closure = the entire space (like the rationals on the line). Those would pass your test, but surely your momma ain't of measure zero?
A) Your momma is so fat her closure consists of *her* interior points only, or
B) Your momma is so fat her complement is of category zero.
Alternative A is more in the spirit of this thread, but it does allow your momma to be empty...
To which a guy would say: I didn't allow your momma to be empty last night.
I died laughing
Gotta love a gal who can take a tasteless math pun and run with it.