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Unique a -closure for some -groups of rational valued functions

Anthony W. Hager, Chawne M. Kimber, Warren W. McGovern (2005)

Czechoslovak Mathematical Journal

Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct a -closures. Here, we find a reasonably large class with unique and perfectly describable a -closure, the class of archimedean -groups with weak unit which are “ -convex”. ( is the group of rationals.) Any C ( X , ) is -convex and its unique a -closure is the Alexandroff algebra of functions on X defined from the clopen sets; this is sometimes C ( X ) .

Universal meager F σ -sets in locally compact manifolds

Taras O. Banakh, Dušan Repovš (2013)

Commentationes Mathematicae Universitatis Carolinae

In each manifold M modeled on a finite or infinite dimensional cube [ 0 , 1 ] n , n ω , we construct a meager F σ -subset X M which is universal meager in the sense that for each meager subset A M there is a homeomorphism h : M M such that h ( A ) X . We also prove that any two universal meager F σ -sets in M are ambiently homeomorphic.

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