I started this thread to post questions about words...not math :P.
I understand what this means but they call it a projection map. Is there something else that goes along with than meets the eyes?
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)