Universal Wightman field

The weak nuclearity of the trial function space Usub(F)sup(n) for the universal class Usub(F)sup(n*) is proved and the notion of complex-spread concentration in the universal class Usub(F)sup(no) of operator-valued generalized functions is introduced. On this basis both the local commutativity axiom and the broken local commutativity axiom for the operator-repres field phi .. . . are formulated, the Poincare invariant of the theory being held. These formulations demand neither finite trial functions, nor the reduction of the field phi to Borel's sets