Geography Reference
In-Depth Information
fulfills
(i)
M
0
=
∅
,
(ii)
M
i
∩
M
j
=
∅
(
i, j
∈{
1
,
2
,
3
}
,i
=
j
)
,
(A.16)
N
∗
.
(iii)
M
=
M
1
∪
M
2
∪
M
3
=
End of Example.
Exercise A.3 (Fibering).
Find
three
fibres of the set of
M
=
{
M
0
,M
1
,M
2
}
.
(A.17)
Answer :
M
0
:= 3
Z
:=
{
x
|
3
y
=
x
and
y
∈
Z
}
=
=
{
...,
−
6
,
−
3
,
0
,
3
,
6
,...
}
,
M
1
:= 3
Z
+1:=
{
x
|
3
y
+1=
x
and
y
∈
Z
}
=
(A.18)
=
{
...,
−
5
,
−
2
,
1
,
4
,
7
,...
}
,
M
2
:= 3
Z
+2:=
{
x
|
3
y
+2=
x
and
y
∈
Z
}
=
=
{
...,
−
4
,
−
1
.
2
,
5
,
8
,...
}
.
End of Exercise.
Example A.6 (Hasse diagram, lexicographic order).
The
Hasse diagram
of a
lexicographic order
in a set of words which begin with the initial letter
“a” is called a chain. That is, all elements are ordered along a half line or line; there are no
bifurcations: compare with Fig.
A.10
.
Fig. A.10.
Hasse diagram, lexicographic order
End of Example.
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