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V
n
A
n
m (m ) A
n
L
m
M
0
A
n
π = {M ∈ A
n
|
−−−→
M
0
M ∈ L
m
}.
m {M
0
, L
m
}
m π = {M
0
, L
m
} M
1
∈ π
{M
1
, L
m
} = {M
0
, L
m
} m π
L
m
M
0
M
M
1
M ∈ {M
1
, L
m
}⇐⇒
−−−→
M
1
M ∈
L
m
⇐⇒
−−−→
M
0
M
1
+
−−−→
M
1
M ∈ L
m
−−−→
M
0
M
1
∈
L
m
(V
n
, +) ⇐⇒
−−−→
M
0
M ∈ L
m
⇐⇒ M ∈ {M
0
, L
m
}
π = {M
0
, L
m
} m
(A
n
, V
n
, ψ) ψ
π
= ψ|π × π : π × π → V
n
.
ψ
π
(π × π) ⊂ L
m
ψ
π
: π × π → L
m
(π, L
m
, ψ
π
) m
A, B ∈ π =⇒
−−→
M
0
A,
−−−→
M
0
B ∈ L
m
=⇒
−→
AB =
−−−→
M
0
B −
−−→
M
0
A ∈ L
m
M
0
A
B
A ∈ π v ∈ L
m
1
◦
B ∈ A
n
−→
AB = v
−−−→
M
0
B =
−−→
M
0
A +
−→
AB ∈ L
m
=⇒ B ∈ π
1
◦
π 2
◦
π
A
n
π ⊂ A
n
L
m
⊂ V
n
(π, L
m
, ψ
π
)
m A
n
m
A
n
m
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efghifjbhikgd Lm w efgrgntqmu smfml igsv} M0 w bjlckjmiht homn}{qmm
egndbgymhikg k An ~
−−−→
π = {M ∈ An | M0 M ∈ Lm }.
+-E,5)57> m .6-/1-/7> +2D*: /6*D20: -+35E-:~ {M , L } <
XYZ[¡Y\]Y^ }hi ljnjbj m peoghvghi π = {M , L } a M ∈ π
0 m
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egnp
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1 m 0 m
£¤Y[¥^ M ∈ {M , L } ⇐⇒ − −−→
M1 M ∈
Lm ⇐⇒ M0 M1 +M1 M ∈ Lm 751 151 M0 M1 ∈
1 m
M1 −−−→ −−−→ −−−→
M Lm 0 (Vn , +) F 932..5 .- /6-*,0 ⇐⇒
M0 M ∈ Lm ⇐⇒ M ∈ {M0 , Lm } <
M0 −−−→
XYZ[¡Y\]Y^ }hi π = {M , L } m peoghvghi k j``abbgd efgp
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0 m
¦ ψ (π × π) ⊂ L aw homngkjimobgw ψ : π × π → L
§ ¢πfguvj (π, L ,mψ ) j``abbgm efghifjbhikg
π
fjldmfbghia
m
m
£¤Y[¥^ 2/7> A, B ∈ π =⇒ −
m π
−→ −−−→ −→
M0 A, M0 B ∈ Lm =⇒ AB =
M0 B − M0 A ∈ Lm <
−−−→ −−→
2/7>
G A ∈ π 0 v ∈ Lm < -9D5 /2*
B
/7B2*7 .- 51/0-:* 1◦ *D0,/7B*,,58 7-)15
A ) −→ −−−→
B ∈ An 75158 7- AB = v < - M0 B =
M0
M0 A + AB ∈ Lm =⇒ B ∈ π < 510: -+35
−−→ −→
E-: 51/0-:5 1◦ BA.-6,8*7/8 D68 π < 1/0-:5 2◦ BA.-6,8*7/8 D68 7-)*1
.30,5D6*50C .6-/1-/70 π .-/1-6>12 -,5 BA.-6,8*7/8 D68 B/*C 7-)*1
50,,-9- .3-/735,/7B5 An <
VWXYZY[Y\]Y^ gndbgymhikg π ⊂ A ijvgmw sig not bmvgigfgxg
Lm ⊂ Vn ifg uv j (π, Lm , ψπ ) tkotmiht j``abbcd
n
efghifjbhikgdw bjp
lckjmiht m pdmfbcd egnefghifjbhikgd k An
E D-15E5,,-9- BA* .3*D6-*,08 /6*D2*7 )7- m :*3,A:0 .-D.3-
/735,/7B5:0 B An 8B687/8 m .6-/1-/70 ¨7-9- .3-/735,/7B5 0 7-6>1- -,0 <
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