| Title:
|
On (transfinite) small inductive dimension of products (English) |
| Author:
|
Chatyrko, V. A. |
| Author:
|
Kozlov, K. L. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
41 |
| Issue:
|
3 |
| Year:
|
2000 |
| Pages:
|
597-603 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
transfinite dimension |
| MSC:
|
54F45 |
| idZBL:
|
Zbl 1038.54012 |
| idMR:
|
MR1795088 |
| . |
| Date available:
|
2009-01-08T19:05:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119192 |
| . |
| Reference:
|
[1] Basmanov V.N.: On inductive dimensions of products of spaces.Moscow Univ. Math. Bull. 36 (1981), 1 19-22. MR 0613119 |
| Reference:
|
[2] Chatyrko V.A.: Ordinal products of topological spaces.Fund. Math. 144 (1994), 95-117. Zbl 0809.54027, MR 1273690 |
| Reference:
|
[3] Chatyrko V.A.: On finite sum theorems for transfinite inductive dimensions.Fund. Math., to appear. Zbl 0938.54031, MR 1734819 |
| Reference:
|
[4] Engelking R.: Theory of Dimensions, Finite and Infinite.Heldermann Verlag, Lemgo, 1995. Zbl 0872.54002, MR 1363947 |
| Reference:
|
[5] Filippov V.V.: On the inductive dimension of the product of bicompacta.Soviet Math. Dokl. 13 (1972), 250-254. Zbl 0243.54032 |
| Reference:
|
[6] Hessenberg G.: Grundbegriffe der Mengenlehre.Göttingen, 1906. |
| Reference:
|
[7] Lifanov I.K.: On the dimension of the product of one-dimensional bicompacta.Soviet Math. Dokl. 9 (1968), 648-651. |
| Reference:
|
[8] Malyhin D.V.: Some properties of topological products (in Russian).Moscow State University, Dissertation, 1999. |
| Reference:
|
[9] Pasynkov B.A.: On inductive dimensions.Soviet Math. Dokl. 10 (1969), 1402-1406. Zbl 0205.52803, MR 0254821 |
| Reference:
|
[10] Toulmin G.H.: Shuffling ordinals and transfinite dimension.Proc. London Math. Soc. 4 (1954), 177-195. Zbl 0055.41406, MR 0065907 |
| Reference:
|
[11] Vinogradov R.N.: On transfinite dimension.Moscow Univ. Math. Bull. 48 (1993), 5 15-17. MR 1355765 |
| Reference:
|
[12] Zarelua A.V.: On a theorem of Hurewicz.Amer. Math. Soc. Transl. 55 (1966), 2 141-152. |
| . |
