Ellis D.B. Automorphisms and equivalence relations in topological dynamics / D.B.Ellis, R.Ellis. - Cambridge: Cambridge university press, 2014. - xiv, 268 p. - (London Mathematical Society lecture note series; 412). - Bibliogr.: p.264-265. - Ind.: p.266-268. - ISBN 978-1-107-63322-3 Шифр: (Pr 1123/412) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Introduction ................................................... ix PART I. UNIVERSAL CONSTRUCTIONS ................................. 1 1 The Stone-cech compactification βT ........................... 3 Appendix ..................................................... 7 2 Flows and their enveloping semigroups ....................... 19 3 Minimal sets and minimal right ideals ....................... 27 4 Fundamental notions ......................................... 37 5 Quasi-factors and the circle operator ....................... 54 Appendix .................................................... 60 PART II. EQUIVALENCE RELATIONS AND AUTOMORPHISMS OF FLOWS ...... 65 6 Quotient spaces and relative products ....................... 67 7 Icers on M and automorphisms of M ........................... 83 8 Regular flows .............................................. 103 9 The quasi-relative product ................................. 111 PART III. THE τ-TOPOLOGY ...................................... 125 10 The т-topology on Aut(X) ................................... 127 11 The derived group .......................................... 138 12 Quasi-factors and the τ-topology ........................... 149 PART IV. SUBGROUPS OF G AND THE DYNAMICS OF MINIMAL FLOWS ..... 155 13 The proximal relation and the group P ...................... 157 14 Distal flows and the group D ............................... 167 15 Equicontinuous flows and the group E ....................... 178 Appendix ................................................... 193 16 The regionally proximal relation ........................... 203 PART V. EXTENSIONS OF MINIMAL FLOWS ........................... 209 17 Open and highly proximal extensions ........................ 211 Appendix ................................................... 222 18 Distal extensions of minimal flows ......................... 229 19 Almost periodic extensions of minimal flows ................ 242 20 A tale of four theorems .................................... 257 References .................................................... 264 Index ......................................................... 266