Title

Composition-closed ℓ-groups of almost-piecewise-linear functions

Document Type

Article

Publication Date

9-1-2011

Abstract

In the present work, we shall construct some non-essential H-closed epireflections of W that are not comparable with any other known H-closed epireflections of W other than the divisible hull and the epicompletion. We show first that the free objects in any H-closed epireflective subcategory must be closed under composition (see Section 2 for a precise definition), and that any epic extension of a free W-object on n generators that is closed under composition is actually the free object on n generators in some H-closed epireflective subcategory of W. We then apply these results to certain ℓ-groups of almost-piecewise-linear Baire functions on R{double-struck}. By definition, a function f:R{double-struck}→R{double-struck} is almost-piecewise-linear if there is a finite point set S⊂R{double-struck} such that f is piecewise-linear on the complement of any neighborhood of S. © 2011 Elsevier B.V.

Publication Source (Journal or Book title)

Topology and its Applications

First Page

1902

Last Page

1908

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