X Preface The book is intended for readers familiar with the basic notions of geom- etry, linear algebra, and analysis. In particular, some knowledge of open, closed, and compact sets in Euclidean space is assumed. The book contains many problems, which the reader is invited to think about. They are divided into three groups: (1) exercises solving them should not cause any difficulties, so their solutions are not included (2) prob- lems they are not so easy, and the solutions to most of them are given at the end of the book (3) challenging problems (marked with an asterisk) each of these problems is the content of a whole scientific paper. They are formulated as problems not to overburden the main text of the book. The solutions to most of these problems are also given at the end of the book. The problems are based on the first- and second-year graduate topology courses taught by the author at the Independent University of Moscow in 2002. This work was financially supported by the Russian Foundation for Basic Research (project no. 05-01-01012a).

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