| Title:
|
Completion theorem for uniform entropy (English) |
| Author:
|
Kimura, Takashi |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
389-399 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Modifying Bowen's entropy, we introduce a new uniform entropy. We prove that the completion theorem for uniform entropy holds in the class of all metric spaces. However, the completion theorem for Bowen's entropy does not hold in the class of all totally bounded metric spaces. (English) |
| Keyword:
|
entropy |
| Keyword:
|
completion |
| Keyword:
|
uniformity |
| MSC:
|
28D20 |
| MSC:
|
54C70 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 0937.54024 |
| idMR:
|
MR1651987 |
| . |
| Date available:
|
2009-01-08T18:41:26Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119016 |
| . |
| Reference:
|
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| Reference:
|
[AM] Aarts J.M., Martens M.: Flows on one-dimensional spaces.Fund. Math. 131 (1988), 53-67. Zbl 0677.54032, MR 0970914 |
| Reference:
|
[AO] Aarts J.M., Oversteegen L.G.: On one-to-one continuous images of $\Bbb R$.Topology Appl. 41 (1991), 17-23. MR 1129695 |
| Reference:
|
[AKM] Adler R.L., Konheim A.G., McAndrew M.H.: Topological entropy.Trans. Amer. Math. Soc. 114 (1965), 309-319. Zbl 0127.13102, MR 0175106 |
| Reference:
|
[B] Bowen R.: Entropy for group endomorphisms and homogeneous spaces.Trans. Amer. Math. Soc. 153 (1971), 401-414. Zbl 0212.29201, MR 0274707 |
| Reference:
|
[DGS] Denker M., Grillenberger C., Sigmund K.: Ergodic Theory on Compact Spaces.Lecture Notes in Math. 527, Springer, Berlin-Heidelberg-New York, 1976. Zbl 0328.28008, MR 0457675 |
| Reference:
|
[E] Engelking R.: General Topology.Heldermann, Berlin, 1989. Zbl 0684.54001, MR 1039321 |
| Reference:
|
[M] Morita K.: On the simple extension of a space with respect to a uniformity. I, II, III, IV.Proc. Japan Acad. 27 (1951), 65-72, 130-137, 166-171, 632-636. MR 0048782 |
| Reference:
|
[W] Walters P.: Ergodic Theory - Introductory Lectures.Lecture Notes in Math. 458, Springer, Berlin-Heidelberg-New York, 1975. Zbl 0299.28012, MR 0480949 |
| . |
