Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

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

100%

Komisarski A.

Fundamenta Mathematicae

2006

tom 189

nr 2

149-154

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.

Functions Equivalent to Borel Measurable Ones

51%

Komisarski A., Michalewski H., Milewski P.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

tom 58

nr 1

55-64

Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Fundamenta Mathematicae

2 Komisarski A.

1 Michalewski H.

1 Milewski P.

1 2010

1 2006

Wyniki wyszukiwania

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

Functions Equivalent to Borel Measurable Ones