I would say both or either.
For me, if you can have sex outside the relationship, then the relationship isn't closed.
However, my problem with closed relationship is that I feel it tells me I'm not allowed to fall in love, which isn't under my control and therefore doesn't seem fair.
So I would say a relationship can be opened one way, the other, or both, but can only be considered closed if neither are allowed.
Me: 31F, straight
Seamus: My husband, 32M, straight
Dragon: My boyfriend, 29M, pansexual, married to Fox
Fox: My boyfriend, 29M, homoflexible, married to Dragon