Mathematics Faculty Articles

Title

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 -groups with designated weak unit and complete -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 Wand 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 -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).

Comments

2010 Mathematics Subject Classification

Primary 06F20, 54G99, 18A40

Secondary 06B23, 54G05

DOI

10.2478/s12175-011-0019-0

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