Category:Topologically Equivalent Metrics
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This category contains results about Topologically Equivalent Metrics in the context of Metric Spaces.
$d_1$ and $d_2$ are topologically equivalent if and only if:
- For all metric spaces $\struct {B, d}$ and $\struct {C, d'}$:
- For all mappings $f: B \to A$ and $g: A \to C$:
- $(1): \quad f$ is $\tuple {d, d_1}$-continuous if and only if $f$ is $\tuple {d, d_2}$-continuous
- $(2): \quad g$ is $\tuple {d_1, d'}$-continuous if and only if $g$ is $\tuple {d_2, d'}$-continuous.
Such mappings $f$ and $g$ can be referred to as homeomorphisms.
Also see
Category:Homeomorphisms for the wider concept of homeomorphisms between topological spaces.
Subcategories
This category has only the following subcategory.
Pages in category "Topologically Equivalent Metrics"
The following 11 pages are in this category, out of 11 total.