Let the topological space X be $\displaystyle \Re$ with the finite complement topology, and let the topological space Y be $\displaystyle \Re$ with the discrete topology. Define a function

f: X---> Y byf(x)= $\displaystyle \Re$ - {x}. So, for example, If

U = $\displaystyle \Re$ -C, whereC= {$\displaystyle {x_1,......,x_n}$}, thenf(U) =C

(a) Isfcontinuous?Why or why not?

(b) What is $\displaystyle f^-1$?Is it continuous or not?

(c) Isfa homeomorphism? Why or why not?

Please help me out