◀ ▲ ▶Branches / Topology / Proposition: Metric Spaces are Hausdorff Spaces

Proposition: Metric Spaces are Hausdorff Spaces

Let \((X,d)\) be a metric space. Then any two distinct points \(x,y\in X\) with \(x\neq y\) have also distinct neighborhoods \(U,V\), i.e. \(U\cap V=\emptyset\).

\((X,d)\) is then called a Hausdorff space.

Table of Contents

Proofs: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

1. Forster Otto: "Analysis 2, Differentialrechnung im \(\mathbb R^n\), Gewöhnliche Differentialgleichungen", Vieweg Studium, 1984