Metrizable implies monotonically 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 must also satisfy the second topological space property
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Statement

Any metrizable space is monotonically normal. In fact, we can construct an explicit monotone normality operator using the metric.

Definitions used

Metrizable space

Further information: Metrizable space

Monotonically normal space

Further information: Monotonically normal space