I'm not sure I understand what you're asking for... Are you wondering if there is an application of this ?
I can show you one (the first that came in my mind), but it has to do with measure theory (product sigma-algebra). So if you're interested, I can show it...
And Opalg once used them to explain stuff in product topology.
There another way of seeing these functions, it's calling them the coordinates mappings :
(note that it's
and not
, I don't know how you learnt it, but my teachers always used the second one for defining the function)