The same effect can be replicated in Oracle either by using the first_value() function or by using one of the rank() or row_number() functions.
Both variants also work in Postgres.
first_value()
select distinct col1,
first_value(col2) over (partition by col1 order by col2 asc)
from tmp
first_value gives the first value for the partition, but repeats it for each row, so it is necessary to use it in combination with distinct to get a single row for each partition.
row_number() / rank()
select col1, col2 from (
select col1, col2,
row_number() over (partition by col1 order by col2 asc) as rownumber
from tmp
) foo
where rownumber = 1
Replacing row_number() with rank() in this example yields the same result.
A feature of this variant is that it can be used to fetch the first N rows for a given partition (e.g. “last 3 updated”) simply by changing rownumber = 1 to rownumber <= N.