Hey I don't know if anyone can help but here goes:I need to proof these 3 statements:

Let X have a discrete topolgy and Y be an arbitrary topological space. Show that every funtion f:X maps to Y is continuous.

Let y have the trivial topology and X be an arbitrary topological space. Show that every funtion f: X map to Y is coninuous.

Let X & Y be topological spaces. A function f:X maps to Y is continuous if and only in the inverse (C) is closed in X for every closed set C is a subset of Y.