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