Book Problem Books in Mathematics: A Cp-Theory Problem Book : Functional Equivalencies 0 by Vladimir V. Tkachuk in PDF, EPUB
9783319243832 3319243837 This fourth volume in Vladimir Tkachuk's series on "Cp"-theory gives reasonably complete coverage of the theoryof functional equivalenciesthrough 500 carefully selected problems and exercises. By systematically introducing each of the major topics of "Cp"-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of "t"-equivalent, "u"-equivalent and"l"-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems anddimension theory. Moreover, the inclusion of Kolmogorov'ssolution of Hilbert's Problem 13 is included as it is needed forthepresentation of the theory of"l"-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by "t"-equivalence, Okunev's method of constructing"l"-equivalent spaces and the theorem of Marciszewski and Pelant on"u"-invariance of absolute Borel sets.", This is the fourth volume of Tkachuk's problem books on Cp-Theory andgives a reasonably complete coverage of the theoryof functional equivalenciesthrough 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of "t"-equivalent, "u"-equivalent and "l"-equivalent spaces is developed from scratch. For the sake of self-containment, the reader will find an introduction to the theory of uniform spaces, the theory of locally convex spaces as well as to the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov'ssolution of Hilbert's Problem 13 is included as it is needed forthepresentation of the theory of "l"-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Krupski's theorem on preservation of Lebesgue dimension by "t"-equivalence, Okunev's method of constructing "l"-equivalent spaces and the theorem of Marciszewski and Pelant on "u"-invariance of absolute Borel sets."
9783319243832 3319243837 This fourth volume in Vladimir Tkachuk's series on "Cp"-theory gives reasonably complete coverage of the theoryof functional equivalenciesthrough 500 carefully selected problems and exercises. By systematically introducing each of the major topics of "Cp"-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of "t"-equivalent, "u"-equivalent and"l"-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems anddimension theory. Moreover, the inclusion of Kolmogorov'ssolution of Hilbert's Problem 13 is included as it is needed forthepresentation of the theory of"l"-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by "t"-equivalence, Okunev's method of constructing"l"-equivalent spaces and the theorem of Marciszewski and Pelant on"u"-invariance of absolute Borel sets.", This is the fourth volume of Tkachuk's problem books on Cp-Theory andgives a reasonably complete coverage of the theoryof functional equivalenciesthrough 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research.The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of "t"-equivalent, "u"-equivalent and "l"-equivalent spaces is developed from scratch. For the sake of self-containment, the reader will find an introduction to the theory of uniform spaces, the theory of locally convex spaces as well as to the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov'ssolution of Hilbert's Problem 13 is included as it is needed forthepresentation of the theory of "l"-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Krupski's theorem on preservation of Lebesgue dimension by "t"-equivalence, Okunev's method of constructing "l"-equivalent spaces and the theorem of Marciszewski and Pelant on "u"-invariance of absolute Borel sets."