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 offers kind of entire assurance of the theory of practical equivalencies through 500 conscientiously chosen difficulties and routines. by way of systematically introducing all the significant themes of Cp-theory, the ebook is meant to convey a devoted reader from simple topological ideas to the frontiers of contemporary research. The ebook provides whole and updated info at the protection of topological homes through homeomorphisms of functionality areas.  An exhaustive idea of t-equivalent, u-equivalent and l-equivalent areas is built 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 speculation of inverse structures and dimension idea. in addition, the inclusion of Kolmogorov's solution of Hilbert's challenge thirteen is incorporated because it is required for the presentation of the speculation of l-equivalent areas. This quantity includes crucial classical effects on practical equivalencies, in particular,  Gul'ko and Khmyleva's instance of  non-preservation of  compactness by way of 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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