Mathematics Faculty Articles
Functorial Polar Functions
Document Type
Article
Publication Date
6-1-2011
Publication Title
Mathematica Slovaca
Keywords
Polar functions, Functorial polar functions, Covering functions, Functorial covering functions, Reflective hull classes, Coreflective covering classes
ISSN
0139-9918
Volume
61
Issue/No.
3
First Page
389
Last Page
410
Abstract
W∞ denotes the category of archimedean ℓ-groups with designated weak unit and complete ℓ-homomorphisms that preserve the weak unit. CmpT2,∞ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on W∞ and its dual a functorial covering function on CmpT2,∞.
We demonstrate that functorial polar functions give rise to reflective hull classes in W∞ and that functorial covering functions give rise to coreflective covering classes in CmpT2,∞. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal α, the class of α-projectable ℓ-groups is reflective in W∞, and the class of α-disconnected compact Hausdorff spaces is coreflective in CmpT2,∞. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).
NSUWorks Citation
Carrera, Ricardo Enrique, "Functorial Polar Functions" (2011). Mathematics Faculty Articles. 60.
https://nsuworks.nova.edu/math_facarticles/60
DOI
10.2478/s12175-011-0019-0
Comments
2010 Mathematics Subject Classification
Primary 06F20, 54G99, 18A40
Secondary 06B23, 54G05