# Normality is not hereditary

From Topospaces

This article gives the statement, and possibly proof, of a topological space property (i.e., normal space)notsatisfying a topological space metaproperty (i.e., subspace-hereditary property of topological spaces).

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This article gives the statement and possibly, proof, of a non-implication relation between two topological space properties. That is, it states that every topological space satisfying the first topological space property (i.e., Normal space (?)) neednotsatisfy the second topological space property (i.e., Hereditarily normal space (?))

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## Statement

It is possible to have a normal space and a subset of such that is not a normal space in the subspace topology.

In other words, it is possible to have a normal space that is not a hereditarily normal space.