Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers

Table 1

Notation in 𝛼-arithmetic and 𝛽-arithmetic.

	𝛼-arithmetic	𝛽-arithmetic
Realm	𝐴	𝐵
Addition	+̇	+̈
Subtraction	−̇	−̈
Multiplication	×̇	×̈
Division	/̇	/̈
Ordering	≤̇	≤̈