Create Dimension - Functional Dependency Between Levels

the literature equates dimension hierarchies with fuctional dependencies between the levels. I like to tst the strength of this assumption with the implementation of 'CREATE DIMENSION' which allows you to create roll-up hierarchies.

My question to put it simply is this: Given:

CREATE DIMENSION location_dim
LEVEL location IS (location.loc_id)
LEVEL city IS (location.city)
LEVEL state IS (location.state)
HIERARCHY geog_rollup (
location CHILD OF
city CHILD OF
state CHILD
)

Can I insert the following rows into the dimension:
loc_id, city, state
1, Epping, NSW
2, Epping, VIC

Please note that the two Eppings are different cities.

Given the roll-up hierarchy City -> State, will it require that for every city there can be only one state in which case the FD between City and State cannot hold. Or, is it that the roll-up hierarchy defined here has nothing to do with FD.

The second part of the question is if the answer to the above question is that the roll-up is not the same as FD, then is the ATTRIBUTE clause meant to define the n:1 (functional dependency) instead?