Profinite semigroups and symbolic dynamics. (2020)
- Record Type:
- Book
- Title:
- Profinite semigroups and symbolic dynamics. (2020)
- Main Title:
- Profinite semigroups and symbolic dynamics
- Further Information:
- Note: Jorge Almeida, Alfredo Costa, Revekka Kyriakoglou, Dominique Perrin.
- Other Names:
- Almeida, Jorge
Costa, Alfredo
Kyriakoglou, Revekka
Perrin, Dominique - Contents:
- Intro -- Contents -- 1 Introduction -- 2 Prelude: Profinite Integers -- 2.1 Introduction -- 2.2 Profinite Integers -- 2.3 Profinite Natural Integers -- 2.4 Zero Set of a Recognizable Series -- 2.5 Odometers -- 2.6 Exercises -- 2.6.1 Section 2.2 -- 2.6.2 Section 2.3 -- 2.6.3 Section 2.4 -- 2.7 Solutions -- 2.7.1 Section 2.2 -- 2.7.2 Section 2.3 -- 2.7.3 Section 2.4 -- 2.8 Notes -- 3 Profinite Groups and Semigroups -- 3.1 Introduction -- 3.2 Topological and Metric Spaces -- 3.2.1 Topological Spaces -- Definition and First Examples -- Nets -- Continuity -- 3.2.2 Metric Spaces 3.13.1 Section 3.2 -- 3.13.2 Section 3.3 -- 3.13.3 Section 3.5 -- 3.13.4 Section 3.6 -- 3.13.5 Section 3.7 -- 3.13.6 Section 3.8 -- 3.13.7 Section 3.9 -- 3.13.8 Section 3.12 -- 3.14 Solutions -- 3.14.1 Section 3.2 -- 3.14.2 Section 3.3 -- 3.14.3 Section 3.5 -- 3.14.4 Section 3.6 -- 3.14.5 Section 3.7 -- 3.14.6 Section 3.8 -- 3.14.7 Section 3.9 -- 3.14.8 Section 3.12 -- 3.15 Notes -- 4 Free Profinite Monoids, Semigroups and Groups -- 4.1 Introduction -- 4.2 Free Monoids and Semigroups -- 4.3 Free Groups -- 4.4 Free Profinite Monoids and Semigroups -- 4.5 Pseudowords as Operations 4.6 Free Profinite Groups -- 4.7 Presentations of Profinite Semigroups -- 4.8 Profinite Codes -- 4.9 Relatively Free Profinite Monoids and Semigroups -- 4.10 Exercises -- 4.10.1 Section 4.2 -- 4.10.2 Section 4.3 -- 4.10.3 Section 4.4 -- 4.10.4 Section 4.5 -- 4.10.5 Section 4.6 -- 4.10.6 Section 4.7 -- 4.10.7 Section 4.8 -- 4.10.8Intro -- Contents -- 1 Introduction -- 2 Prelude: Profinite Integers -- 2.1 Introduction -- 2.2 Profinite Integers -- 2.3 Profinite Natural Integers -- 2.4 Zero Set of a Recognizable Series -- 2.5 Odometers -- 2.6 Exercises -- 2.6.1 Section 2.2 -- 2.6.2 Section 2.3 -- 2.6.3 Section 2.4 -- 2.7 Solutions -- 2.7.1 Section 2.2 -- 2.7.2 Section 2.3 -- 2.7.3 Section 2.4 -- 2.8 Notes -- 3 Profinite Groups and Semigroups -- 3.1 Introduction -- 3.2 Topological and Metric Spaces -- 3.2.1 Topological Spaces -- Definition and First Examples -- Nets -- Continuity -- 3.2.2 Metric Spaces 3.13.1 Section 3.2 -- 3.13.2 Section 3.3 -- 3.13.3 Section 3.5 -- 3.13.4 Section 3.6 -- 3.13.5 Section 3.7 -- 3.13.6 Section 3.8 -- 3.13.7 Section 3.9 -- 3.13.8 Section 3.12 -- 3.14 Solutions -- 3.14.1 Section 3.2 -- 3.14.2 Section 3.3 -- 3.14.3 Section 3.5 -- 3.14.4 Section 3.6 -- 3.14.5 Section 3.7 -- 3.14.6 Section 3.8 -- 3.14.7 Section 3.9 -- 3.14.8 Section 3.12 -- 3.15 Notes -- 4 Free Profinite Monoids, Semigroups and Groups -- 4.1 Introduction -- 4.2 Free Monoids and Semigroups -- 4.3 Free Groups -- 4.4 Free Profinite Monoids and Semigroups -- 4.5 Pseudowords as Operations 4.6 Free Profinite Groups -- 4.7 Presentations of Profinite Semigroups -- 4.8 Profinite Codes -- 4.9 Relatively Free Profinite Monoids and Semigroups -- 4.10 Exercises -- 4.10.1 Section 4.2 -- 4.10.2 Section 4.3 -- 4.10.3 Section 4.4 -- 4.10.4 Section 4.5 -- 4.10.5 Section 4.6 -- 4.10.6 Section 4.7 -- 4.10.7 Section 4.8 -- 4.10.8 Section 4.9 -- 4.11 Solutions -- 4.11.1 Section 4.2 -- 4.11.2 Section 4.3 -- 4.11.3 Section 4.4 -- 4.11.4 Section 4.5 -- 4.11.5 Section 4.6 -- 4.11.6 Section 4.7 -- 4.11.7 Section 4.8 -- 4.11.8 Section 4.9 -- 4.12 Notes -- 5 Shift Spaces -- 5.1 Introduction 5.2 Factorial Sets -- 5.3 Shift Spaces -- 5.4 Block Maps and Conjugacy -- 5.5 Substitutive Shift Spaces -- 5.5.1 Primitive Substitutions -- 5.5.2 Matrix of a Substitution -- 5.5.3 Recognizable Substitutions -- 5.6 The Topological Closure of a Uniformly Recurrent Set -- 5.6.1 Uniformly Recurrent Pseudowords -- 5.6.2 The J-Class of a Uniformly Recurrent Set -- 5.7 Generalization to Recurrent Sets -- 5.8 Exercises -- 5.8.1 Section 5.2 -- 5.8.2 Section 5.3 -- 5.8.3 Section 5.5 -- 5.8.4 Section 5.6 -- 5.8.5 Section 5.7 -- 5.9 Solutions -- 5.9.1 Section 5.2 -- 5.9.2 Section 5.3 -- 5.9.3 Section 5.5 … (more)
- Publisher Details:
- Cham, Switzerland : Springer
- Publication Date:
- 2020
- Extent:
- 1 online resource
- Subjects:
- 512.2
Semigroups
Set theory
Computer science -- Mathematics
Dynamics
Ergodic theory
Group theory
Logic, Symbolic and mathematical
Electronic books
Electronic books - Languages:
- English
- ISBNs:
- 9783030552152
3030552152 - Related ISBNs:
- 3030552144
9783030552145 - Notes:
- Note: Includes bibliographical references and index.
- Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.550969
- Ingest File:
- 04_030.xml