MATH 2000A - Fall 2014
Due beginning of class on Friday, September 19.
1. Determine if the following sets are open, closed or neither and justify your answer.
(b) cfw_x R2 | x1 + x2 = 1 R2
(c) (a1 , b1 ) (an , bn ) = cfw_x Rn | ak < x
Solutions to the assignment
1. (a) f : R R2 such that
f (t) =
1 + t2 t + 1
We claim that (0, 0) is the limit point of the range of f although it is not contained in
the range set. Hence range of f is not closed in R2 .
Consider the point