Download PDF - On finite sum theorems for transfinite inductive dimensionsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On finite sum theorems for transfinite inductive dimensions

Authors 1

Affiliations

  1. Department of Mathematics, Linkeping University, 581 83 Linkeping, Sweden

Abstract

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 Sα,α<ω1, given by Luxemburg [Lu2].

Keywords

ENG
transfinite dimension

Bibliography

  1. [Ch] V. A. Chatyrko, Ordinal products of topological spaces, Fund. Math. 144 (1994), 95-117.
  2. [Ch-K] V. A. Chatyrko and K. L. Kozlov, On ( transfinite) small inductive dimension of products, preprint, 1999.
  3. [E] R. Engelking, Theory of Dimensions, Finite and Infinite, Heldermann Verlag, Lemgo, 1995.
  4. [F] V. V. Filippov, A bicompactum with noncoinciding inductive dimensions, Soviet Math. Dokl. 10 (1969), 208-211.
  5. [Le] B. T. Levshenko, Spaces of transfinite dimensions, Mat. Sb. 67 (1965), 225-266 (in Russian).
  6. [Lu1] L. A. Luxemburg, Compacta with noncoinciding transfinite dimensions, Soviet Math. Dokl. 14 (1973), 1593-1597.
  7. [Lu2] L. A. Luxemburg, On compact metric spaces with noncoinciding transfinite dimensions, Pacific J. Math. 93 (1981), 339-386.
  8. [S] Ju. M. Smirnov, On universal spaces for certain classes of infinite-dimensional spaces, Izv. Akad. Nauk SSSR 23 (1959), 185-196 (in Russian).
Fundamenta Mathematicae
1999/162/1
Export to PBN, Opens in new tab
Pages:
91-98
Main language of publication
English
Received
1999-02-16
Accepted
1999-05-10
Published
1999
Exact and natural sciences