It is known that [there are only 14 reasonable tensor norms](http://arxiv.org/pdf/1101.4195.pdf) in $Ban$. On the other hand it is well known fact for topologists that [one can obtain only 14 different sets](http://en.wikipedia.org/wiki/Kuratowski%27s_closure-complement_problem) from a given set applying closure and complementation operations.


It seems like a pure coincidence but... both constructions starts with the single object (a set/ the injective tensor norm), then apply only predescribed operations (closure and complement/ transpose, dual and right projective associate) and get only 14 different objects in the end.


Is this a simple coincidence or there is something deep behind the scenes? Maybe someone knows other examples?



Is Grothendieck classification of tensor norms and Kuratowski's 14 sets theorem somehow related?
I asked David Sherman this question and this was his response:


In the Kuratowski setup, if you omit complementation, you get 7 elements. Adding complementation gives you a disjoint upside-down copy.


In the Grothendieck setup, if you omit duality, you get 8 elements (two five-element chains with common inf and sup, like an O). Adding duality gives you an upside-down copy, but it is not disjoint -- two elements agree between the copies. ''


So, it seems that the answer is NO.


