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On finite sum theorems for transfinite inductive dimensions

100%

Chatyrko V. A.

Fundamenta Mathematicae

1999

tom 162

nr 1

91-98

We discuss the exactness of estimates in the finite sum theorems for transfinite inductive dimensions trind and trInd. The technique obtained gives an opportunity to repeat and sometimes strengthen some well known results about compacta with trind ≠ trInd. In particular we improve an estimate of the small transfinite inductive dimension of Smirnov's compacta $S^α, α < ω_1$, given by Luxemburg [Lu2].

On weakly infinite-dimensional subspuees

63%

Borst P.

Fundamenta Mathematicae

1991-1992

tom 140

nr 3

225-235

We will construct weakly infinite-dimensional (in the sense of Y. Smirnov) spaces X and Y such that Y contains X topologically and $dim Y = ω_0$ and $dim X = ω_0 + 1$. Consequently, the subspace theorem does not hold for the transfinite dimension dim for weakly infinite-dimensional spaces.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Borst P.

1 Chatyrko V. A.

1 1999

1 1992

Wyniki wyszukiwania

On finite sum theorems for transfinite inductive dimensions

On weakly infinite-dimensional subspuees