# Continuously

## Definition

### First-order Continuous Micro

Sets Vector Space

,
. Then, for any
,
is a linear mapping of
. If
to all linear mapping of
is
. The
is a mapping from
, if this mapping is a continuous map, it is called
Yes from
< SECTION> to
Continuously multi-mapped. Generally, all consecutive micromalable collections on
are generally recorded
, so
. ### High-order Continuous Micro

Set Vector Space

,
>
in
< / Section> The n-order Continuously Microprecognition is
, which is the element exists in
exists and all elements in
, ie
,
The component of
and
.

## correlation theorem

Clairore Theorem (1 order)

set vector space

, < Section> ,
When and only when all of the
exists and continuous. As you can see from this theorem, all consecutive functions of
can be recorded as
. This combines the high-order continuous recursive definition of the previous high-end, and can obtain a continuous additional equivalent definition:
is from
to
Continuously can be micromaled, which means all of the biasing numbers of
exists and continuous.

Clairore Theorem (N-order)

Set of vector space

,
, ifSection> , the n-order n-order deflection exchange of
remains unchanged during the order of order, ie
remains not in
Change,
is a differential operator and
.

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