Transcription of General Topology
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General Topology
Part 1. General Topology The goal of this part of the book is to teach the language of math- ematics. More speci cally, one of its most important components: the language of set-theoretic Topology , which treats the basic notions related to continuity. The term General Topology means: this is the Topology that is needed and used by most mathematicians. A permanent usage in the capacity of a common mathematical language has polished its system of de nitions and theorems. Nowadays, studying General Topology really more resembles studying a language rather than mathematics: one needs to learn a lot of new words, while proofs of most theorems are extremely simple. On the other hand, the theorems are numerous because they play the role of rules regulating usage of words. We have to warn the students for whom this is one of the rst math- ematical subjects. Do not hurry to fall in love with it, do not let an imprinting happen. This eld may seem to be charming, but it is not very active.
The goal of this part of the book is to teach the language of math-ematics. More specifically, one of its most important components: the language of set-theoretic topology, which treats the …
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