On (transfinite) small inductive dimension of products

Vitalij A. Chatyrko; Konstantin L. Kozlov

Commentationes Mathematicae Universitatis Carolinae (2000)

  • Volume: 41, Issue: 3, page 597-603
  • ISSN: 0010-2628

Abstract

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In this paper we study the behavior of the (transfinite) small inductive dimension ( t r i n d ) i n d on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of t r i n d for Cartesian products.

How to cite

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Chatyrko, Vitalij A., and Kozlov, Konstantin L.. "On (transfinite) small inductive dimension of products." Commentationes Mathematicae Universitatis Carolinae 41.3 (2000): 597-603. <http://eudml.org/doc/248579>.

@article{Chatyrko2000,
abstract = {In this paper we study the behavior of the (transfinite) small inductive dimension $(trind)$$ind$ on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of $trind$ for Cartesian products.},
author = {Chatyrko, Vitalij A., Kozlov, Konstantin L.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {transfinite dimension},
language = {eng},
number = {3},
pages = {597-603},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On (transfinite) small inductive dimension of products},
url = {http://eudml.org/doc/248579},
volume = {41},
year = {2000},
}

TY - JOUR
AU - Chatyrko, Vitalij A.
AU - Kozlov, Konstantin L.
TI - On (transfinite) small inductive dimension of products
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2000
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 41
IS - 3
SP - 597
EP - 603
AB - In this paper we study the behavior of the (transfinite) small inductive dimension $(trind)$$ind$ on finite products of topological spaces. In particular we essentially improve Toulmin’s estimation [T] of $trind$ for Cartesian products.
LA - eng
KW - transfinite dimension
UR - http://eudml.org/doc/248579
ER -

References

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  2. Chatyrko V.A., Ordinal products of topological spaces, Fund. Math. 144 (1994), 95-117. (1994) Zbl0809.54027MR1273690
  3. Chatyrko V.A., On finite sum theorems for transfinite inductive dimensions, Fund. Math., to appear. Zbl0938.54031MR1734819
  4. Engelking R., Theory of Dimensions, Finite and Infinite, Heldermann Verlag, Lemgo, 1995. Zbl0872.54002MR1363947
  5. Filippov V.V., On the inductive dimension of the product of bicompacta, Soviet Math. Dokl. 13 (1972), 250-254. (1972) Zbl0243.54032
  6. Hessenberg G., Grundbegriffe der Mengenlehre, Göttingen, 1906. 
  7. Lifanov I.K., On the dimension of the product of one-dimensional bicompacta, Soviet Math. Dokl. 9 (1968), 648-651. (1968) 
  8. Malyhin D.V., Some properties of topological products (in Russian), Moscow State University, Dissertation, 1999. 
  9. Pasynkov B.A., On inductive dimensions, Soviet Math. Dokl. 10 (1969), 1402-1406. (1969) Zbl0205.52803MR0254821
  10. Toulmin G.H., Shuffling ordinals and transfinite dimension, Proc. London Math. Soc. 4 (1954), 177-195. (1954) Zbl0055.41406MR0065907
  11. Vinogradov R.N., On transfinite dimension, Moscow Univ. Math. Bull. 48 (1993), 5 15-17. (1993) MR1355765
  12. Zarelua A.V., On a theorem of Hurewicz, Amer. Math. Soc. Transl. 55 (1966), 2 141-152. (1966) 

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