A Cp-Theory Problem Book

Functional Equivalencies
Softcover Nachdruck of the original 1. Auflage 2016
ISBN: 978-3-319-79616-1
Verlag: Springer International Publishing

Buch, Englisch, 727 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 11051 g

Reihe: Problem Books in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Tkachuk, Vladimir V.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie

Inhaltsverzeichnis

Preface.-Detailed summary of exercise sections.-Introduction.-1. Properties Preserved by Homeomorphisms of Function Spaces.-2. Solutions of Problems 1-500.-3. Bonus Results: Some Hidden Statements.-4. Open Problems.-Bibliography.-List of Special Symbols.-Index.

Über Autor(innen)

Vladimir V. Tkachuk is a professor in the Department of Mathematics of the Autonomous Metropolitan University in Mexico City. He holds a PhD from Moscow State University and is the author of
 A Cp-Theory Problem Book: Compactness in Function Spaces
(Springer, 2015)
, A Cp-Theory Problem Book: Special Features of Function Spaces
 (Springer, 2014) and 
A Cp-Theory Problem Book: Topological and Function Spaces
 (Springer, 2011). All volumes have published in the Problem Books in Mathematics series.