I would like to answer this question from a mathematical point of view.
The word "openness" means something that is real and correlated with some other aspects. Let's assume a 3 dimensional space.
If we would like to choose the other dimensions as perpendicular to this first one, we could simply define them by their correlation with the first one being 0.
The definition is mathematic. Given a vector finding ortogonal ones means finding something that could exist or not in the nature.
Given 5 dimensions which are correlated and really exists (i.e. the big five traits), we could easily find a new space made by one real dimension and 4 dimension ortogonal to the first one which doesn't exist in the reality.
Then we could project every person analisys from the Big Five Space to the second perfectly orthogonal space.
Every dimension of the second space could be also defined as a mix of the dimensions of the first space.
You could ask for a better answer here but I hope something of what I said was clear.