Can a function map into or out of the null set?

[Gear300]

Can a function involve a mapping into or out of a null set?

 

[jbunniii]

See here:

http://en.wikipedia.org/wiki/Empty_function

 

[CRGreathouse]

Can a function involve a mapping into or out of a null set?

Out of: yes, but it doesn't do anything (in an even more literal sense than the identity function doesn't do anything).

Into: Yes, but if it's a function rather than a partial function the domain must have exactly zero elements (because if it had even one it would have needed to map that to something).

So in both cases it's just the empty function, as jbunniii points out.