Titlebook: Topology; An Introduction Stefan Waldmann Textbook 2014 Springer International Publishing Switzerland 2014 Point Set Topology.Topological S

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Topological Spaces and Continuity,Starting from metric spaces as they are familiar from elementary calculus, one observes that many properties of metric spaces like the notions of continuity and convergence do not depend on the detailed information about the metric: instead, only the coarser knowledge of the set of open subsets is needed.

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Construction of Topological Spaces,For a topological space . we have already seen that any subset . inherits a topology, the subspace topology .. This provides one important construction of topologies on certain sets. In this chapter we collect several further general constructions.

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Convergence in Topological Spaces,In this chapter we will consider sequences in topological spaces and their convergence. For metric spaces, sequences will be the appropriate tool to study all phenomena of convergence and continuity.

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Introduction,s to obtain again open subsets, and the empty set as well as the total space are open, too. This already provides the precise definition of a topology, i.e. a collection of subsets of a set . which should be regarded as “open”.

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Textbook 2014 etc. Topology is a fundamental tool in most branches of pure mathematics and is also omnipresent in more applied parts of mathematics. Therefore students will need fundamental topological notions already at an early stage in their bachelor programs..While there are already many excellent monographs

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