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

.