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.
