Functorial polar functions

Rok, strany: 2011, 389 - 410

$\mathbf{W}_∞$ denotes the category of archimedean $\ell$-groups with designated weak unit and complete $\ell$-homomorphisms that preserve the weak unit. $\mathbf{CmpT}_2,∞$ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on $\mathbf{W}_∞$ and its dual a functorial covering function on $\mathbf{CmpT}_2,∞$. We demonstrate that functorial polar functions give rise to reflective hull classes in $\mathbf{W}_∞$ and that functorial covering functions give rise to coreflective covering classes in $\mathbf{CmpT}_2,∞$. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal $α$, the class of $α$-projectable $\ell$-groups is reflective in $\mathbf{W}_∞$, and the class of $α$-disconnected compact Hausdorff spaces is coreflective in $\mathbf{CmpT}_2,∞$. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).

ISO 690:

Carrera, R. 2011. Functorial polar functions. In Mathematica Slovaca, vol. 61, no.3, pp. 389-410. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0019-0

APA:

Carrera, R. (2011). Functorial polar functions. Mathematica Slovaca, 61(3), 389-410. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0019-0