Source Word
inverse limit
Noun
(algebra)
A
subset
of
the
Cartesian
product
of
all
the
members
of
an
inverse
system,
such
that
a
member
M
of
the
subset
is
a
sort
of
“cross
section”
of
the
inverse
system
(as
fiber
bundle)
induced
by
the
morphisms
of
it.
(If
i<j
in
the
indexing
poset
then
f_ij:A_j→A_i
in
the
inverse
system
and
if
a_i∈A_i,
a_j∈A_j
are
components
of
M
then
f_ij(a_j)=a_i).
Japanese Meaning
数学（特に代数学や位相数学）において、逆系（射影系）の各対象のデカルト積のうち、各成分がインデックスにおける順序関係に従って射（モルフィズム）により結び付けられ、あたかも断面（クロスセクション）のような性質を持つ部分集合を指す。
Sense（1）
(algebra)
A
subset
of
the
Cartesian
product
of
all
the
members
of
an
inverse
system,
such
that
a
member
M
of
the
subset
is
a
sort
of
“cross
section”
of
the
inverse
system
(as
fiber
bundle)
induced
by
the
morphisms
of
it.
(If
i<j
in
the
indexing
poset
then
f_ij:A_j→A_i
in
the
inverse
system
and
if
a_i∈A_i,
a_j∈A_j
are
components
of
M
then
f_ij(a_j)=a_i).
（ plural ）
