Mathematics Faculty Articles

Title

Pointfree Functorial Polar Functions

Document Type

Article

Publication Date

2-1-2016

Publication Title

Applied Categorical Structures

Keywords

Pointfree polar functions, Functorial polar functions, Hull class, Skeletal maps, Compact regular frame, α-disconnected frame, α-cloz frame

ISSN

0927-2852

Volume

24

Issue/No.

1

First Page

37

Last Page

52

Abstract

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.

DOI

10.1007/s10485-014-9385-4