This is totally dependant on your philosophy and what you mean
by this question. Simply, the world CAN exist without man (as it
did for billions of years before us, and more than likely will
continue to exist without us), and man could exist without
"world".
Looking deeper, and if by "world", you mean "culture" (or some
analog thereof), it is because the very definition of "culture"
requires the action of "man". Conversely, everyone draws on
"culture" ("world") in some fashion.