Consider f(x) = 1/(1+x^2) as a function from R to R with the usual metric. Are the following statements true or false (give proofs or counterexamples):
1. f(A) is open for all open sets A in R
2. f(A) is open for all closed sets A in R
thanks!
Consider f(x) = 1/(1+x^2) as a function from R to R with the usual metric. Are the following statements true or false (give proofs or counterexamples):
1. f(A) is open for all open sets A in R
2. f(A) is open for all closed sets A in R
thanks!