Topological spaces

"For any algebraic objects we can introduce the discrete topology, under which the algebraic operations are continuous functions. This leads to concepts such as topological groups, topological vector spaces, topological rings and local fields."
Kool! That means I can have a discrete topology and define continuous functions in it. And the continuous functions are the algebraic operations. And there's more: any function from a discrete topological space to another topological space is continuous.