diff options
| author | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-29 17:32:24 +0100 |
|---|---|---|
| committer | Justin Gassner <justin.gassner@mailbox.org> | 2024-02-29 17:32:24 +0100 |
| commit | a1b5de688d879069b5e1192057d71572c7bc5368 (patch) | |
| tree | a0f4801d14bfbcc75a6091bdc7d17aceab71f6d4 /pages/general-topology/metric-spaces/index.md | |
| parent | 8b9bb9346c217874670b0f1798ab6f1cb28fdb83 (diff) | |
| download | site-a1b5de688d879069b5e1192057d71572c7bc5368.tar.zst | |
Update
Diffstat (limited to 'pages/general-topology/metric-spaces/index.md')
| -rw-r--r-- | pages/general-topology/metric-spaces/index.md | 10 |
1 files changed, 9 insertions, 1 deletions
diff --git a/pages/general-topology/metric-spaces/index.md b/pages/general-topology/metric-spaces/index.md index 52b2b4c..6aef400 100644 --- a/pages/general-topology/metric-spaces/index.md +++ b/pages/general-topology/metric-spaces/index.md @@ -60,8 +60,16 @@ Let $(X,d)$ be a (semi-)metric space. The proofs are straightforward. +{% definition Isometry %} +Suppose $(X,d_X)$ and $(Y,d_Y)$ are metric spaces. +We say that a mapping $f : X \to Y$ is *isometric* or an *isometry* if it obeys +$d_Y \big\lparen f(x),f(x') \big\rparen = d_X(x,x')$ for all $x,x' \in X$. +{% enddefinition %} + +As a consequence of **(M1)**, +every isometry is injective. + TODO -- isometry - metric induced by a norm - metric product |