Hausdorff implies T1

This article gives the statement and possibly, proof, of an implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Hausdorff space) must also satisfy the second topological space property (i.e., T1 space)
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Statement

Any Hausdorff space is a T1 space.

Related facts

• Hausdorff implies US
• Hausdorff implies KC
• Hausdorff implies sober
• T1 not implies Hausdorff
• KC not implies Hausdorff
• US not implies Hausdorff

Proof

The proof is direct from the definitions.