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Chapter: Basic Topological Concepts
We start with some basic concepts of topology. Please note that the term topology has double meaning. The first meaning of this term is mathematical discipline "topology" itself. But "topology" also means  in its second meaning  one of the key concepts in this discipline. We will use the term sometimes in the first and sometimes in the second meaning, and it will be clear from the context, which meaning is meant.
Table of Contents
Explanations: 1
 Definition: Topological Space, Topology
 Proposition: Clopen Sets and Boundaries
 Definition: Discrete and Indiscrete Topology
 Definition: Ordering of Topologies
 Definition: Open, Closed, Clopen
 Proposition: Alternative Characterization of Topological Spaces
 Definition: Neighborhood
 Proposition: Properties of the Set of All Neighborhoods of a Point
 Proposition: A Necessary Condition of a Neighborhood to be Open
 Definition: Boundary Points, Closures, Interiors, and Exteriors
 Proposition: How the Boundary Changes the Property of a Set of Being Open
 Definition: Regular Open, Regular Closed
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Chapters: 1
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References
Bibliography
 Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
 Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition