Let A be an infinite union of singleton sets in the topological space Y. A is open in the topological space Y.(a) Isfcontinuous?Why or why not?

However, is not necessarily open in X.

Thus, f is not continuous.

f^-1 is continuous since the domain of f^-1 is given by the discrete topology (verify this)(b) What is ?Is it continuous or not?

f is not a homeomorphism, because f is not continuous.(c) Isfa homeomorphism? Why or why not?