On finite sum theorems for transfinite inductive dimensions

• Autorzy: Vitalij A. Chatyrko
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

transfinite dimension

Kategorie tematyczne

• 54F45: Dimension theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 162
• Numer: 1
• Strony: 91-98

Daty

wydano

1999

otrzymano

1999-02-16

poprawiono

1999-05-10

poprawiono

1999-06-07

Twórcy

autor

Vitalij A. Chatyrko

• Department of Mathematics, Linkeping University, 581 83 Linkeping, Sweden

Bibliografia

• [Ch] V. A. Chatyrko, Ordinal products of topological spaces, Fund. Math. 144 (1994), 95-117.
• [Ch-K] V. A. Chatyrko and K. L. Kozlov, On ( transfinite) small inductive dimension of products, preprint, 1999.
• [E] R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann Verlag, Lemgo, 1995.
• [F] V. V. Filippov, A bicompactum with noncoinciding inductive dimensions, Soviet Math. Dokl. 10 (1969), 208-211.
• [Le] B. T. Levshenko, Spaces of transfinite dimensions, Mat. Sb. 67 (1965), 225-266 (in Russian).
• [Lu1] L. A. Luxemburg, Compacta with noncoinciding transfinite dimensions, Soviet Math. Dokl. 14 (1973), 1593-1597.
• [Lu2] L. A. Luxemburg, On compact metric spaces with noncoinciding transfinite dimensions, Pacific J. Math. 93 (1981), 339-386.
• [S] Ju. M. Smirnov, On universal spaces for certain classes of infinite-dimensional spaces, Izv. Akad. Nauk SSSR 23 (1959), 185-196 (in Russian).