Ultrafilters and topologies on groups / Yevhen G. Zelenyuk.

Format:

Book

Author/Creator:

Zelenyuk, Yevhen G.

Contributor:

Hazel M. Hussong Fund.

Series:

De Gruyter expositions in mathematics ; 50.

De Gruyter expositions in mathematics ; 50

Language:

English

Subjects (All):

Topological group theory.

Ultrafilters (Mathematics).

Physical Description:

viii, 219 pages : illustrations ; 25 cm.

Place of Publication:

Berlin ; New York : De Gruyter, [2011]

Contents:

1 Topological Groups 1

1.1 The Notion of a Topological Group 1

1.2 The Neighborhood Filter of the Identity 4

1.3 The Topology T(F) 7

1.4 Topologizing a Group 10

1.5 Metrizable Refinements 14

1.6 Topologizability of a Countably Infinite Ring 18

2 Ultrafilters 26

2.1 The Notion of an Ultrafilter 26

2.2 The Space βD 29

2.3 Martin's Axiom 34

2.4 Ramsey Ultrafilters and P-points 36

2.5 Measurable Cardinals 39

3 Topological Spaces with Extremal Properties 41

3.1 Filters and Ultrafilters on Topological Spaces 41

3.2 Spaces with Extremal Properties 42

3.3 Irresolvability 46

4 Left Invariant Topologies and Strongly Discrete Filters 52

4.1 Left Topological Semigroups 52

4.2 The Topology T[F] 54

4.3 Strongly Discrete Filters 56

4.4 Invariant Topologies 63

5 Topological Groups with Extremal Properties 68

5.1 Extremally Disconnected Topological Groups 68

5.2 Maximal Topological Groups 71

5.3 Nodec Topological Groups 72

5.4 P-point Theorems 76

6 The Semigroup βS 82

6.1 Extending the Operation to βS 82

6.2 Compact Right Topological Semigroups 86

6.3 Hindman's Theorem 91

6.4 Ultrafilters from K(βS) 94

7 Ultrafilter Semigroups 97

7.1 The Semigroup Ult(T) 97

7.2 Regularity 101

7.3 Homomorphisms 105

8 Finite Groups in βG 110

8.1 Local Left Groups and Local Homomorphisms 110

8.2 Triviality of Finite Groups in βZ 117

8.3 Local Automorphisms of Finite Order 120

8.4 Finite Groups in G* 128

9 Ideal Structure of βG 130

9.1 Left Ideals 130

9.2 Right Ideals 136

9.3 The Structure Group of K(βG) 140

9.4 K(βG) is not Closed 144

10 Almost Maximal Topological Groups 147

10.1 Construction 147

10.2 Properties 150

10.3 Semilattice Decompositions and Burnside Semigroups 154

10.4 Projectives 158

10.5 Topological Invariantness of Ult(T) 165

11 Almost Maximal Spaces 170

11.1 Right Maximal Idempotents in H_k 170

11.2 Projectivity of Ult(T) 174

11.3 The Semigroup C(p) 177

11.4 Local Monomorphisms 181

12 Resolvability 188

12.1 Regular Homeomorphisms of Finite Order 188

12.2 Resolvability of Topological Groups 194

12.3 Absolute Resolvability 198

13 Open Problems 208.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

3110204223

OCLC:

695560026

Publisher Number:

99945804791