Manuscript En06-A@1 · En06-A.tex · section · e04c9892

The metric envelope

Order-theoretic and metric domains of dependence › The metric envelope · lines 534–548

En06-A@1#eq:metricenvelope

The triangle inequality gives

N_{s} (Y) \subseteq {x : d (x, Y) \leq r (T - s)} .

For terminal site $A$ , let $I_{s} = B_{d} (A, r (T - s))$ . If a block meets $I_{s + 1}$ , then it lies in $I_{s}$ : for $z \in b \cap I_{s + 1}$ and $w \in b$ ,

d (w, A) \leq d (w, z) + d (z, A) \leq r + r (T - s - 1) .

Displayed formulas in this passage

En06-A@1#eq:metricenvelope · line 537
$N_{s} (Y) \subseteq {x : d (x, Y) \leq r (T - s)} .$
unlabeled · line 545
$d (w, A) \leq d (w, z) + d (z, A) \leq r + r (T - s - 1) .$

Nearby in this section

theorem: Theorem: Exact metric cone
section: The metric envelope