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.