{"title":"Alexander Kharazishvili","description":null,"products":[{"product_id":"introduction-to-combinatorial-methods-in-geometry-book-alexander-kharazishvili-9781032594705","title":"Introduction to Combinatorial Methods in Geometry","description":"\u003cp\u003eThis book offers an introduction to some combinatorial (also, set-theoretical) approaches and methods in geometry of the Euclidean space \u003cb\u003eR\u003c\/b\u003e\u003ci\u003em\u003c\/i\u003e. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry.\u003c\/p\u003e\u003cp\u003eThe author’s primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics: the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc.\u003c\/p\u003e\u003cp\u003eAll chapters (and also the five Appendices) end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exercises vary in their difficulty. Among them there are almost trivial, standard, nontrivial, rather difficult, and difficult. As a rule, more difficult exercises are marked by asterisks and are provided with necessary hints.\u003c\/p\u003e\u003cp\u003eThe material presented is based on the lecture course given by the author. The choice of material serves to demonstrate the unity of mathematics and variety of unexpected interrelations between distinct mathematical branches.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51017893282065,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51017895346449,"sku":"NIN9781032594705","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52597813281041,"sku":"NLS9781032594705","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1032594705.jpg?v=1793728418"},{"product_id":"notes-on-real-analysis-and-measure-theory-book-alexander-kharazishvili-9783031170355","title":"Notes on Real Analysis and Measure Theory","description":"Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52152011260177,"sku":"NLS9783031170355","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031170355.jpg?v=1785819231"},{"product_id":"nonmeasurable-sets-and-functions-book-alexander-kharazishvili-9780444516268","title":"Nonmeasurable Sets and Functions","description":"The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-measurable cardinals;3. The theory of invariant (quasi-invariant)extensions of invariant (quasi-invariant) measures.These topics are under consideration in the book. The role of nonmeasurable sets (functions) in point set theory and real analysis is underlined and various classes of such sets (functions) are investigated . Among them there are: Vitali sets, Bernstein sets, Sierpinski sets, nontrivial solutions of the Cauchy functional equation, absolutely nonmeasurable sets in uncountable groups, absolutely nonmeasurable additive functions, thick uniform subsets of the plane, small nonmeasurable sets, absolutely negligible sets, etc. The importance of properties of nonmeasurable sets for various aspects of the measure extension problem is shown. It is also demonstrated that there are close relationships between the existence of nonmeasurable sets and some deep questions of axiomatic set theory, infinite combinatorics, set-theoretical topology, general theory of commutative groups. Many open attractive problems are formulated concerning nonmeasurable sets and functions.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52427513856273,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52427514478865,"sku":"NLS9780444516268","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780444516268.jpg?v=1759161229"},{"product_id":"lectures-on-real-valued-functions-book-alexander-kharazishvili-9783031953682","title":"Lectures on Real-valued Functions","description":"In diesem Ratgeber wird das l stige Thema Bewerben das erste Mal einfach, lustig und vor allem realit tsnah erkl rt  Daf r verwendet die Autorin den passenden und alltagstauglichen Vergleich zum Dating. Bei potenziellen Partner*innen pr fen, verh ren und verwerfen wir, bis wir uns entscheiden. Aber wenn es um die Suche nach dem Traumjob geht, sind wir oft weniger anspruchsvoll. Warum eigentlich? Als erfolgreiche Karriereberaterin und erfahrene Jobcoachin verr t dir Asmahan Gamgami: welche Anspr che du an deinen Traumjob stellen solltest was deine Bewerbungsunterlagen unwiderstehlich macht warum Recruiter*innen spezialisiert aufs Tindern sind wie du mit Diskriminierung im Kennenlernprozess umgehen kannst wann du aus einer ungl cklichen Arbeitsbeziehung ausbrechen solltest was Dick-Pics mit Stellenausschreibungen zu tun haben","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52476085534993,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52476086649105,"sku":"NLS9783031953682","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031953682.jpg?v=1791924996"},{"product_id":"notes-on-real-analysis-and-measure-theory-book-alexander-kharazishvili-9783031170324","title":"Notes on Real Analysis and Measure Theory","description":"Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52481563230481,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52481564279057,"sku":"NLS9783031170324","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783031170324.jpg?v=1786700240"},{"product_id":"strange-functions-in-real-analysis-book-alexander-kharazishvili-9781498773140","title":"Strange Functions in Real Analysis","description":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eStrange Functions in Real Analysis, Third Edition\u003c\/em\u003e\u003c\/strong\u003e differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. \u003c\/p\u003e\u003cp\u003eAfter introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum.\u003c\/p\u003e\u003cp\u003eFinally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. On the whole, the book is devoted to strange functions (and point sets) in real analysis and their applications. \u003c\/p\u003e","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52484414144785,"sku":"NLS9781498773140","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53036602654993,"sku":"NIN9781498773140","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9781498773140.jpg?v=1793719801"},{"product_id":"strange-functions-in-real-analysis-book-alexander-kharazishvili-9781032919881","title":"Strange Functions in Real Analysis","description":"\u003cp\u003e\u003cstrong\u003e\u003cem\u003eStrange Functions in Real Analysis, Third Edition\u003c\/em\u003e\u003c\/strong\u003e differs from the previous editions in that it includes five new chapters as well as two appendices. More importantly, the entire text has been revised and contains more detailed explanations of the presented material. In doing so, the book explores a number of important examples and constructions of pathological functions. \u003c\/p\u003e\u003cp\u003eAfter introducing basic concepts, the author begins with Cantor and Peano-type functions, then moves effortlessly to functions whose constructions require what is essentially non-effective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum.\u003c\/p\u003e\u003cp\u003eFinally, the author considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms. 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