Restricting database access to certain users

I'm looking into migrating several users from MySQL to Postgres and I'm
running into a problem with security.  I don't think I understand how
security is handled within postgres.  I'm using PostgreSQL v7.1.3 on a Red
Hat 7.2 system.

The problem is that there appears to not be a way to prevent users from
accessing each other's databases and creating new objects in them.  As a
test, I created userB and userB and then created databaseA and databaseB.
I then connected to databasea as usera and created a table with one row of
data.  I did the same with databaseb and userb.

Next, I connected to databasea as userb and created a table.  Sure enough,
postgres allowed me to create the table in databasea as userb.  Only userb
could access this table.

I wish to prevent such a situation.  There doesn't seem to be a way to do
so.  I can grant and revoke permissions on tables but not on databases as
a whole.

--
Matt Perry | matt at primefactor dot com