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

• Autorzy: Andrzej Komisarski
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54C35: Function spaces
• 46E25: Rings and algebras of continuous, differentiable or analytic functions
• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 189
• Numer: 2
• Strony: 149-154

Daty

wydano

2006

Twórcy

autor

Andrzej Komisarski

• Department of Probability Theory and Statistics, Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Identyfikatory

DOI

10.4064/fm189-2-4