Monotonically 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., monotonically normal space) must also satisfy the second topological space property (i.e., hereditarily normal space)
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- Monotone normality is hereditary
- Monotonically normal implies collectionwise normal
- Monotonically normal implies hereditarily collectionwise normal
Given: A monotonically normal space .
To prove: Every subspace of is normal.
Proof: By fact (1), every subspace of is monotonically normal. Using fact (2), we obtain that every subspace of is normal.