Proving Openness of $\pi_1$ and $\pi_2$ Maps

[tomboi03]

A map f: X-> Y is said to be an open map if for every open set U of X, the set f(U) is open in Y. Show that \pi₁:X x Y -> X and \pi₂: X x Y -> Y are open maps...


I don't know where to begin with this...
Can someone give me an idea of where to start?

Thank You.

 

[CompuChip]

I suppose that \pi_i is a projection operator, for example
\pi_1: X \times Y \to X: (x, y) \mapsto x

Also you need some information on the topologies. Are X and Y topological spaces and is X x Y endowed with the induced topology (i.e. defined by products of open sets in X and open sets in Y and extended to a topology)?

 

[wofsy]

A map f: X-> Y is said to be an open map if for every open set U of X, the set f(U) is open in Y. Show that \pi₁:X x Y -> X and \pi₂: X x Y -> Y are open maps...


I don't know where to begin with this...
Can someone give me an idea of where to start?

Thank You.

if you carefully look at the definition of an open set in the product topology it will be clear.