Infinite places does not mean everywhere. This is a common misconception when dealing with infinite sets.
Suppose you have infinite many places, as many as the natural numbers.
You may have infinitely many places numbered by even numbers, while still not have the other, infinitely many, places with odd numbers.
So a more correct translation would be "in many places". But then again, if you are talking about infinite sets, the concept of "many" is also tricky, and leads into questions of set cardinality, aleph numbers, etc. which fortunately is a lot more interesting than the usual Netflix soap operas.
Uh, thanks Lars. Where would we be without iconoclastic pedantry on Slashdot?
Since we're being pedantic, you may wish to learn how to parse the phrase "loosely meaning".