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Proposition: A Necessary Condition of a Neighborhood to be Open
If a set $B$ is a neighborhood of all of its points, then it is open. Conversely, if $B$ is closed, then there is a point $A\in B$ such that $B$ is not a neighborhood of it.
Table of Contents
Proofs: 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