Ultrafilters and Topologies on Groups

Preface\nContents\n1 Topological Groups\n	1.1 The Notion of a Topological Group\n	1.2 The Neighborhood Filter of the Identity\n	1.3 The Topology T\r(F)\n	1.4 Topologizing a Group\n	1.5 Metrizable Refinements\n	1.6 Topologizability of a Countably Infinite Ring\n2 Ultrafilters\n	2.1 The Notion of an Ultrafilter\n	2.2 The Space βD\n	2.3 Martin’s Axiom\n	2.4 Ramsey Ultrafilters and P -points\n	2.5 Measurable Cardinals\n3 Topological Spaces with Extremal Properties\n	3.1 Filters and Ultrafilters on Topological Spaces\n	3.2 Spaces with Extremal Properties\n	3.3 Irresolvability\n4 Left Invariant Topologies and Strongly Discrete Filters\n	4.1 Left Topological Semigroups\n	4.2 The Topology T[F]\n	4.3 Strongly Discrete Filters\n	4.4 Invariant Topologies\n5 Topological Groups with Extremal Properties\n	5.1 Extremally Disconnected Topological Groups\n	5.2 Maximal Topological Groups\n	5.3 Nodec Topological Groups\n	5.4 P -point Theorems\n6 The Semigroup βS\n	6.1 Extending the Operation to βS\n	6.2 Compact Right Topological Semigroups\n	6.3 Hindman’s Theorem\n	6.4 Ultrafilters from K(βS)\n7 Ultrafilter Semigroups\n	7.1 The Semigroup Ult(T)\n	7.2 Regularity\n	7.3 Homomorphisms\n8 Finite Groups in βG\n	8.1 Local Left Groups and Local Homomorphisms\n	8.2 Triviality of Finite Groups in βZ\n	8.3 Local Automorphisms of Finite Order\n	8.4 Finite Groups in G*\n9 Ideal Structure of βG\n	9.1 Left Ideals\n	9.2 Right Ideals\n	9.3 The Structure Group of K(βG)\n	9.4 K\r(βG) is not Closed\n10 Almost Maximal Topological Groups\n	10.1 Construction\n	10.2 Properties\n	10.3 Semilattice Decompositions and Burnside Semigroups\n	10.4 Projectives\n	10.5 Topological Invariantness of Ult(T)\n11 Almost Maximal Spaces\n	11.1 Right Maximal Idempotents in HK\n	11.2 Projectivity of Ult(T)\n	11.3 The Semigroup C(p)\n	11.4 Local Monomorphisms\n12 Resolvability\n	12.1 Regular Homeomorphisms of Finite Order\n	12.2 Resolvability of Topological Groups\n	12.3 Absolute Resolvability\n13 Open Problems\nBibliography\nIndex