# Open map

1. Feb 10, 2009

### 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 $$\pi$$1:X x Y -> X and $$\pi$$2: 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.

2. Feb 10, 2009

### 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)?

3. Feb 12, 2009

### wofsy

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