On finite sum theorems for transfinite inductive dimensions

Vitalij Chatyrko

Fundamenta Mathematicae (1999)

  • Volume: 162, Issue: 1, page 91-98
  • ISSN: 0016-2736

Abstract

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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].

How to cite

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Chatyrko, Vitalij. "On finite sum theorems for transfinite inductive dimensions." Fundamenta Mathematicae 162.1 (1999): 91-98. <http://eudml.org/doc/212414>.

@article{Chatyrko1999,
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 $S^α, α < ω_1$, given by Luxemburg [Lu2].},
author = {Chatyrko, Vitalij},
journal = {Fundamenta Mathematicae},
keywords = {transfinite dimension; finite sum theorem; Smirnov compactum},
language = {eng},
number = {1},
pages = {91-98},
title = {On finite sum theorems for transfinite inductive dimensions},
url = {http://eudml.org/doc/212414},
volume = {162},
year = {1999},
}

TY - JOUR
AU - Chatyrko, Vitalij
TI - On finite sum theorems for transfinite inductive dimensions
JO - Fundamenta Mathematicae
PY - 1999
VL - 162
IS - 1
SP - 91
EP - 98
AB - 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].
LA - eng
KW - transfinite dimension; finite sum theorem; Smirnov compactum
UR - http://eudml.org/doc/212414
ER -

References

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  1. [Ch] V. A. Chatyrko, Ordinal products of topological spaces, Fund. Math. 144 (1994), 95-117. Zbl0809.54027
  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. Zbl0872.54002
  4. [F] V. V. Filippov, A bicompactum with noncoinciding inductive dimensions, Soviet Math. Dokl. 10 (1969), 208-211. Zbl0186.27002
  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. Zbl0292.54044
  7. [Lu2] L. A. Luxemburg, On compact metric spaces with noncoinciding transfinite dimensions, Pacific J. Math. 93 (1981), 339-386. Zbl0397.54048
  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). Zbl0086.36804

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