Permissions for /tmp

[Jardine@t-online.de (moron)]

I'm trying to find my way around Debian (hamm) and see that a user cannot
use man, which is refused permission to create a /tmp file.  Changing
permissions with >chmod a+w /tmp< from root solves the problem.  (I tried
creating a /tmp directory in my home directory but it didn't work.)   It
makes me wonder:
a: If it's safe to do this, why is this not the default permission?
b: If not, how does a user on a multi-user system (mine isn't) get to man
without root rights?
c: Should I do it another way?

David