Perfectly normal implies hereditarily normal

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., perfectly normal space) must also satisfy the second topological space property (i.e., hereditarily normal space)
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Statement

Any perfectly normal space is a hereditarily normal space -- every subspace of it is a normal space.

Related facts

• Metrizable implies hereditarily normal
• Monotonically normal implies hereditarily normal

Facts used

1. Perfect normality is hereditary
2. Perfectly normal implies normal

Proof

By fact (1), every subspace of a perfectly normal space is perfectly normal, and by fact (2), every subspace is normal.