Category:Isometric Isomorphisms (Normed Division Rings)

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This category contains results about isometric isomorphisms in the context of Normed Division Rings.
Definitions specific to this category can be found in Definitions/Isometric Isomorphisms (Normed Division Rings).

Let $\struct {R, \norm {\,\cdot\,}_R}$ and $\struct {S, \norm {\,\cdot\,}_S}$ be normed division rings.

Let $d_R$ and $d_S$ be the metric induced by the norms $\norm {\,\cdot\,}_R$ and $\norm {\,\cdot\,}_S$ respectively.


Let $\phi:R \to S$ be a bijection such that:

$(1): \quad \phi: \struct {R, d_R} \to \struct {S, d_S}$ is an isometry
$(2): \quad \phi: R \to S$ is a ring isomorphism.

Then $\phi$ is called an isometric isomorphism.


The normed division rings $\struct {R, \norm {\,\cdot\,}_R}$ and $\struct {S, \norm {\,\cdot\,}_S}$ are said to be isometrically isomorphic.

Pages in category "Isometric Isomorphisms (Normed Division Rings)"

The following 2 pages are in this category, out of 2 total.