Manuscript XXII-C@1 · XXII-C.tex · definition · b9a05a24

Definition: Representation-feasibility set

The frozen representation query · lines 784–803

XXII-C@1#def:feasible, XXII-C@1#eq:proper-injective, XXII-C@1#eq:faithful, XXII-C@1#eq:span

Let $A_{m} (D)$ be the set of maps $ι : E_{D} \to R^{m}$ satisfying:

ι is injective and K_{ι} is proper, x ⪯_{D} y ⟺ ι (y) - ι (x) \in K_{ι}, R^{m} = span {ι (y) - ι (x) : x, y \in E_{D}} .

Together with (eq:generated), these are the faithful, spanning, and generated representation requirements of XXII-A CheungXXIIA (def:representation).

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XXII-C@1#eq:proper-injective · line 788
$ι is injective and K_{ι} is proper, x ⪯_{D} y ⟺ ι (y) - ι (x) \in K_{ι}, R^{m} = span {ι (y) - ι (x) : x, y \in E_{D}} .$
XXII-C@1#eq:faithful · line 788
$ι is injective and K_{ι} is proper, x ⪯_{D} y ⟺ ι (y) - ι (x) \in K_{ι}, R^{m} = span {ι (y) - ι (x) : x, y \in E_{D}} .$
XXII-C@1#eq:span · line 788
$ι is injective and K_{ι} is proper, x ⪯_{D} y ⟺ ι (y) - ι (x) \in K_{ι}, R^{m} = span {ι (y) - ι (x) : x, y \in E_{D}} .$

Definition: Representation-feasibility set

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