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A Cp-Theory Problem Book - Functional Equivalencies (Hardcover, 1st ed. 2016)
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A Cp-Theory Problem Book - Functional Equivalencies (Hardcover, 1st ed. 2016)
Series: Problem Books in Mathematics
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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.
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