LElementary Topology Problem Textbook O. Ya. Viro, O. A. Ivanov, N. Yu. Netsvetaev, V. M. Kharlamov

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Dedicated to the memory of Vladimir Abramovich Rokhlin (1919–1984) – our teacher

Introduction
The subject of the book, Elementary Topology Elementary means close to elements, basics. It is impossible to determine precisely, once and for all, which topology is elementary, and which is not. The elementary part of a subject is the part with which an expert starts to teach a novice. We suppose that our student is ready to study topology. So, we do not try to win her or his attention and benevolence by hasty and obscure stories about misterious and attractive things such as the Klein bottle.1 All in good time: the …ver más…

Some of the notions play a fundamental role in other areas of mathematics, but here they are of minor importance. In a word, the basic line is interrupted by variations wherever possible. The variations are clearly separated from the basic theme by graphical means. The second feature distinguishing the present book from the majority of other textbooks is that proofs are separated from formulations. The book looks nearly as a problem book. It would be easy to make the book looking like hundreds of other mathematical textbooks. For this purpose, it suffices to move all variations to the ends of their sections so that they would look excercises to the basic text, and put the proofs of theorems immediately after their formulations.

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For whom is this book? A reader who has safely reached the university level in her/his education may bravely approach this book. Super brave daredevils may try it even earlier. However, we cannot say that no preliminary knowledge is required. We suppose that the reader is familiar with real numbers. And, surely, with natural, integer, and rational numbers, too. Complex numbers will also do no harm, although one can manage without them in the first part of the book. We assume that the reader is acquainted with naive set theory, but admit that this acquaintance may be superficial. For this reason, we make special set-theoretical digressions where the possession of set theory is particularly desirable. We do