{"product_id":"ultrafilters-and-topologies-on-groups-9783110204223","title":"Ultrafilters and Topologies on Groups","description":"  \u003cmeta http-equiv=\"content-type\" content=\"text\/html; charset=iso-8859-1\"\u003e \u003cmeta content=\"mshtml 6.00.6000.17095\" name=\"generator\"\u003e  \u003cp\u003eThis book presents the relationship between ultrafilters and topologies on groups. It shows how ultrafilters are used in constructing topologies on groups with extremal properties and how topologies on groups serve in deriving algebraic results about ultrafilters.\u003c\/p\u003e \u003cp\u003eThe contents of the book fall naturally into three parts. The first, comprising Chapters 1 through 5, introduces to topological groups and ultrafilters insofar as the semigroup operation on ultrafilters is not required. Constructions of some important topological groups are given. In particular, that of an extremally disconnected topological group based on a Ramsey ultrafilter. Also one shows that every infinite group admits a nondiscrete zero-dimensional topology in which all translations and the inversion are continuous.\u003c\/p\u003e \u003cp\u003eIn the second part, Chapters 6 through 9, the Stone-Cêch compactification \u003cem\u003eβG\u003c\/em\u003e of a discrete group \u003cem\u003eG\u003c\/em\u003e is studied. For this, a special technique based on the concepts of a local left group and a local homomorphism is developed. One proves that if \u003cem\u003eG\u003c\/em\u003e is a countable torsion free group, then \u003cem\u003eβG \u003c\/em\u003econtains no nontrivial finite groups. Also the ideal structure of \u003cem\u003eβG\u003c\/em\u003e is investigated. In particular, one shows that for every infinite Abelian group \u003cem\u003eG\u003c\/em\u003e, \u003cem\u003eβG\u003c\/em\u003e contains 2\u003csup\u003e2\u003c\/sup\u003e\u003cspan lang=\"DE\"\u003e|\u003c\/span\u003eG\u003cspan lang=\"DE\"\u003e|\u003c\/span\u003e minimal right ideals.\u003c\/p\u003e \u003cp\u003eIn the third part, using the semigroup \u003cem\u003eβG\u003c\/em\u003e, almost maximal topological and left topological groups are constructed and their ultrafilter semigroups are examined. Projectives in the category of finite semigroups are characterized. Also one shows that every infinite Abelian group with finitely many elements of order 2 is absolutely \u003cem\u003eω\u003c\/em\u003e-resolvable, and consequently, can be partitioned into \u003cem\u003eω\u003c\/em\u003e subsets such that every coset modulo infinite subgroup meets each subset of the partition.\u003c\/p\u003e \u003cp\u003eThe book concludes with a list of open problems in the field. Some familiarity with set theory, algebra and topology is presupposed. But in general, the book is almost self-contained. It is aimed at graduate students and researchers working in topological algebra and adjacent areas.\u003c\/p\u003e","brand":"Yevhen Zelenyuk","offers":[{"title":"Default Title","offer_id":48260874010875,"sku":"9783110204223","price":300.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0779\/3917\/9771\/files\/CoreSourceHub_f55ebb96-470d-4078-b6c6-8fe474afb37c.jpg?v=1778450447","url":"https:\/\/indiepubs.com\/products\/ultrafilters-and-topologies-on-groups-9783110204223","provider":"IndiePubs","version":"1.0","type":"link"}