Kfagerstrom: Created page with " A topological space $(X,\mathcal{T}_X)$ is metrizable if there is a metric $d$ on $X$ such that $\mathcal{T}_X = \mathcal{T}_d$
2023-01-12T07:17:28Z

Created page with " A topological space <math> (X,\mathcal{T}_X) </math> is metrizable if there is a metric <math>d </math> on <math> X</math> such that <math>\mathcal{T}_X = \mathcal{T}_d </mat..."

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A topological space <math> (X,\mathcal{T}_X) </math> is metrizable if there is a metric <math>d </math> on <math> X</math> such that <math>\mathcal{T}_X = \mathcal{T}_d </math>, where <math> \mathcal{T}_d </math> is the metric topology on <math> X</math> induced by <math> d</math>.

Metrizability is a homeomorphism invariant. Metrizability is not preserved by quotients, continuous images, or continuous preimages. Metrizable spaces are <math> \mathcal{T}_4 </math>.

Metrizability - Revision history