# Category:Metrizable Topologies

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This category contains results about **Metrizable Topologies**.

Let $T = \struct {S, \tau}$ be a topological space.

### Definition 1

$T$ is said to be **metrizable** if and only if there exists a metric $d$ on $S$ such that:

- $\tau$ is the topology induced by $d$ on $S$.

### Definition 2

$T$ is said to be **metrizable** if and only if there exists a metric space $M = \struct{A, d}$ such that:

- $T$ is homeomorphic to the topological space $\struct{A, \tau_d}$

where $\tau_d$ is the topology induced by $d$ on $A$.

## Subcategories

This category has the following 5 subcategories, out of 5 total.

### C

### M

### N

## Pages in category "Metrizable Topologies"

The following 31 pages are in this category, out of 31 total.