PROGRESS UPDATE (Mar 19, 2021):
Completed the draft of the introductory section on superfucntion complete spaces, gatheret some bibliography. The grammar needs alot of work and a deep revision is missing. This is just a preliminary draft. I'm currently working on discussing possible fixes for JmsNxn's idea about diffeomorphisms, bridging the gaps to superfunctions by limit tricks (principal solutions) and Nixon's trick. I've also worked out an interesting algebraic rephrasing of piecewise extension and a novel idea (with proofs) of a canonical extension of iteration from the naturals (the cyclic subgroup) to the centralizer of the imput map. I'll add a sketch of possible abstract treatment of hyperoperations.
When finished, I'll post something more tidy and expand more on JmsNxn comments.
Draft.pdf (Size: 676.85 KB / Downloads: 997)
[WARNING: grammar and formulas were NOT doublechecked, read at you own risk]
Completed the draft of the introductory section on superfucntion complete spaces, gatheret some bibliography. The grammar needs alot of work and a deep revision is missing. This is just a preliminary draft. I'm currently working on discussing possible fixes for JmsNxn's idea about diffeomorphisms, bridging the gaps to superfunctions by limit tricks (principal solutions) and Nixon's trick. I've also worked out an interesting algebraic rephrasing of piecewise extension and a novel idea (with proofs) of a canonical extension of iteration from the naturals (the cyclic subgroup) to the centralizer of the imput map. I'll add a sketch of possible abstract treatment of hyperoperations.
When finished, I'll post something more tidy and expand more on JmsNxn comments.
Draft.pdf (Size: 676.85 KB / Downloads: 997)
[WARNING: grammar and formulas were NOT doublechecked, read at you own risk]
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)