Introduction. It is known that under many conditions, effective operators will be partial recursive, ([MS], [KLS], [L]). On the other hand, certain pathological examples have been constructed by Friedberg [F] and Pour-El [P] to show that effective operators are not always partial recursive. Pour-El has observed that although it is well known that all partial recursive operators are continuous, ...

The largest class of hyperstructures is the Hv-structures, introduced in 1990, which proved to have a lot of applications in mathematics and several applied sciences, as well. Hyperstructures are used in the Lie-Santilli theory focusing to the hypernumbers, called e-numbers. We present the appropriate e-hyperstuctures which are defined using any map, in the sense the derivative map, called thet...