Category:Equivalence of Definitions of Metrizable Topology
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This category contains pages concerning Equivalence of Definitions of Metrizable Topology:
Let $T = \struct {S, \tau}$ be a topological space.
The following definitions of the concept of Metrizable Topology are equivalent:
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 $A$.
Pages in category "Equivalence of Definitions of Metrizable Topology"
The following 4 pages are in this category, out of 4 total.