最終更新日:2022/12/24
We apply this notion to make some observation on subspaces which split off as smooth direct summands (providing examples which illustrate that not all subspaces do), and then to show that the diffeological dual of a finite-dimensional diffeological vector space always has the standard diffeology and in particular, any pseudo-metric on the initial space induces, in the obvious way, a smooth scalar product on the dual..
編集履歴(0)
元となった例文
We
apply
this
notion
to
make
some
observation
on
subspaces
which
split
off
as
smooth
direct
summands
(providing
examples
which
illustrate
that
not
all
subspaces
do),
and
then
to
show
that
the
diffeological
dual
of
a
finite-dimensional
diffeological
vector
space
always
has
the
standard
diffeology
and
in
particular,
any
pseudo-metric
on
the
initial
space
induces,
in
the
obvious
way,
a
smooth
scalar
product
on
the
dual..