Pointfree Functorial Polar Functions

C denotes the category of compact regular frames with frame homomorphisms. A function XX , which assigns to each C-object F a subalgebra of P(F)P(F) that contains the complemented elements of F is said to be a polar function. An essential extension H of F is a XX -splitting frame of F if whenever p∈X(F)p∈X(F) , then the polar generated by p in H is complemented. For F∈ C we examine the least XX -splitting extension and prove that every invariant polar function generates a C-hull class of frames. In addition, we define the concept of a functorial polar function and prove that each functorial polar function generates an epireflective subcategory of the category compact regular frames with skeletal maps.