ebook9783319243856d4325

Description

This fourth volume in Vladimir Tkachuk’s series on Cp-theory gives reasonably complete coverage of the theory¬†of functional equivalencies¬†through 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 and¬†dimension theory. Moreover, the inclusion of Kolmogorov’s¬†solution of Hilbert’s Problem 13 is included as it is needed for¬†the¬†presentation 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.