Hi,
you're question is very particular and I'm not sure it make a sense in a real case, it can be a bug but never found it before because it isn't a real situation, let me explain why:
BPC is used for consolidation, planning, budgeting, cost allocation, financial, etc. where the time dimension is a must, that's why you can create a new appset without this dimension, time is mandatory and is used in all the appsets to distuinguish the periods where you're working.
So, probably yours is only an exercise or BPC is not the right software to do what you want.
If the second try to explain what are you trying to do and maybe someone can help you.
Kind regards
Roberto