Definition
Let
S
be a set and
R
be an equivalence relation on
S
, then for any we call
(
x
∈
S
)
we call the set
(
(
[
x
]
R
)
:=
(
{
(
y
∈
S
)
∣
(
x
R
y
)
}
)
)
the
equivalence class
of
x
(under
R
), and the set
(
(
[
S
]
R
)
:=
(
{
(
[
x
]
R
)
∣
(
x
∈
S
)
}
)
)
the
quotient space
of
S
(under
R
).