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On typical parametrizations of finite-dimensional compacta on the Cantor set

100%

Milewski P.

Fundamenta Mathematicae

2002

tom 174

nr 3

253-261

We prove that if X is a perfect finite-dimensional compactum, then for almost every continuous surjection of the Cantor set onto X, the set of points of maximal order is uncountable. Moreover, if X is a perfect compactum of positive finite dimension then for a typical parametrization of X on the Cantor set, the set of points of maximal order is homeomorphic to the product of the rationals and the Cantor set.

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 Milewski P.

1 Komisarski A.

1 Michalewski H.

1 2010

1 2002

Wyniki wyszukiwania

On typical parametrizations of finite-dimensional compacta on the Cantor set

Functions Equivalent to Borel Measurable Ones