Finegrained 3D differential operators hint at the inevitability of their dual reciprocal portrayals

Extending differential operators during transition from 3D operations to prospective 4D operations imply the need to expand their 4D range far beyond the usual set-theoretical universe from which subsets of the domain are composed. The prospective infrastructural expansion related to the attempted extending of operations virtually requires an extra dual reciprocal space and thus implies presence of a certain multispatial structure of both the mathematical- and the corresponding to it physical reality. At this point the implication is only operational for it is deduced from the attempted extension of operational domain/scope of geometric differential operator, which, in turn, demands an expansion of their range. The necessary presence of an extra space is not being postulated but emerges from comparative evaluations of differential operators. The operational necessity of presence of paired dual reciprocal spaces or quasispatial structures also generalizes contravariance for multispatiality.