Displaying similar documents to “Pasting in multiple categories.”

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

Andrzej Komisarski (2006)

Fundamenta Mathematicae


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.

An approach to covering dimensions

Miroslav Katětov (1995)

Commentationes Mathematicae Universitatis Carolinae


Using certain ideas connected with the entropy theory, several kinds of dimensions are introduced for arbitrary topological spaces. Their properties are examined, in particular, for normal spaces and quasi-discrete ones. One of the considered dimensions coincides, on these spaces, with the Čech-Lebesgue dimension and the height dimension of posets, respectively.