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Displaying similar documents to “Dimension, category and K ( Π , n ) spaces”

On localizations of torsion abelian groups

José L. Rodríguez, Jérôme Scherer, Lutz Strüngmann (2004)

Fundamenta Mathematicae

Similarity:

As is well known, torsion abelian groups are not preserved by localization functors. However, Libman proved that the cardinality of LT is bounded by | T | whenever T is torsion abelian and L is a localization functor. In this paper we study localizations of torsion abelian groups and investigate new examples. In particular we prove that the structure of LT is determined by the structure of the localization of the primary components of T in many cases. Furthermore, we completely characterize...

A connection between multiplication in C(X) and the dimension of X

Andrzej Komisarski (2006)

Fundamenta Mathematicae

Similarity:

Let X be a compact Hausdorff topological space. We show that multiplication in the algebra C(X) is open iff dim X < 1. On the other hand, the existence of non-empty open sets U,V ⊂ C(X) satisfying Int(U· V) = ∅ is equivalent to dim X > 1. The preimage of every set of the first category in C(X) under the multiplication map is of the first category in C(X) × C(X) iff dim X ≤ 1.