A Cp-Theory Problem Book: Functional Equivalencies (Problem by Vladimir V. Tkachuk

By Vladimir V. Tkachuk

This fourth quantity in Vladimir Tkachuk's sequence on Cp-theory provides quite entire insurance of the theory of sensible equivalencies through 500 rigorously chosen difficulties and workouts. by way of systematically introducing all of the significant themes of Cp-theory, the e-book is meant to carry a committed reader from easy topological rules to the frontiers of recent research. The ebook provides whole and up to date details at the protection of topological homes by way of homeomorphisms of functionality areas.  An exhaustive concept of t-equivalent, u-equivalent and l-equivalent areas is constructed from scratch.   The reader also will locate introductions to the idea of uniform areas, the idea of in the neighborhood convex areas, in addition to  the idea of inverse platforms and dimension concept. in addition, the inclusion of Kolmogorov's solution of Hilbert's challenge thirteen is integrated because it is required for the presentation of the speculation of l-equivalent areas. This quantity comprises crucial classical effects on practical equivalencies, in particular,  Gul'ko and Khmyleva's instance of  non-preservation of  compactness through t-equivalence, Okunev's approach to constructing  l-equivalent areas and the concept of Marciszewski and Pelant on u-invariance of absolute Borel sets.

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