Completion theorem for uniform entropy

Takashi Kimura

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 389-399
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Kimura, Takashi. "Completion theorem for uniform entropy." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 389-399. <http://eudml.org/doc/248236>.

@article{Kimura1998,
abstract = {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.},
author = {Kimura, Takashi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {entropy; completion; uniformity; uniformity},
language = {eng},
number = {2},
pages = {389-399},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Completion theorem for uniform entropy},
url = {http://eudml.org/doc/248236},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Kimura, Takashi
TI - Completion theorem for uniform entropy
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 389
EP - 399
AB - 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.
LA - eng
KW - entropy; completion; uniformity; uniformity
UR - http://eudml.org/doc/248236
ER -

References

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  6. Denker M., Grillenberger C., Sigmund K., Ergodic Theory on Compact Spaces, Lecture Notes in Math. 527, Springer, Berlin-Heidelberg-New York, 1976. Zbl0328.28008MR0457675
  7. Engelking R., General Topology, Heldermann, Berlin, 1989. Zbl0684.54001MR1039321
  8. 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. (1951) MR0048782
  9. Walters P., Ergodic Theory - Introductory Lectures, Lecture Notes in Math. 458, Springer, Berlin-Heidelberg-New York, 1975. Zbl0299.28012MR0480949

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