A Cp-Theory Problem Book: Functional Equivalencies: 0 (Problem Books in Mathematics) - Tapa dura

Sinopsis

THIS FOURTH VOLUME IN VLADIMIR TKACHUK'S SERIES ON <I>CP</I>-THEORY GIVES REASONABLY COMPLETE COVERAGE OF THE THEORY&NBSP;OF FUNCTIONAL EQUIVALENCIES&NBSP;THROUGH 500 CAREFULLY SELECTED PROBLEMS AND EXERCISES. BY SYSTEMATICALLY INTRODUCING EACH OF THE MAJOR TOPICS OF <I>CP</I>-THEORY, THE BOOK IS INTENDED TO BRING A DEDICATED READER FROM BASIC TOPOLOGICAL PRINCIPLES TO THE FRONTIERS OF MODERN RESEARCH.&NBSP;THE BOOK PRESENTS COMPLETE AND UP-TO-DATE INFORMATION ON THE PRESERVATION OF TOPOLOGICAL PROPERTIES BY HOMEOMORPHISMS OF FUNCTION SPACES. &NBSP;AN EXHAUSTIVE THEORY OF <I>T</I>-EQUIVALENT,&NBSP;<I>U</I>-EQUIVALENT AND&NBSP;<I>L</I>-EQUIVALENT SPACES IS DEVELOPED FROM SCRATCH. &NBSP; THE READER WILL ALSO FIND INTRODUCTIONS TO THE THEORY OF UNIFORM SPACES, THE THEORY OF LOCALLY CONVEX SPACES, AS WELL AS&NBSP; THE THEORY OF INVERSE SYSTEMS AND&NBSP;DIMENSION THEORY. MOREOVER, THE INCLUSION OF KOLMOGOROV'S&NBSP;SOLUTION OF HILBERT'S PROBLEM 13 IS INCLUDED AS IT IS NEEDED FOR&NBSP;THE&NBSP;PRESENTATION OF THE THEORY OF&NBSP;<I>L</I>-EQUIVALENT SPACES. THIS VOLUME CONTAINS THE MOST IMPORTANT CLASSICAL RESULTS ON FUNCTIONAL EQUIVALENCIES, IN PARTICULAR,&NBSP; GUL'KO AND KHMYLEVA'S EXAMPLE OF &NBSP;NON-PRESERVATION OF&NBSP; COMPACTNESS BY <I>T</I>-EQUIVALENCE, OKUNEV'S METHOD OF CONSTRUCTING&NBSP;&NBSP;<I>L</I>-EQUIVALENT SPACES AND THE THEOREM OF MARCISZEWSKI AND PELANT ON&NBSP;<I>U</I>-INVARIANCE OF ABSOLUTE BOREL SETS.

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