On the basis of the elementary theorem that there is a majorant (minorant)on the nonempty set which must have a superieur (inf erieur), We prove the five character theorems of the continuous functions on the close intervalle.

The illegal saving have several decades of history in China, despite the public security departments,the financial supervision departments,the industrial and commercial administrative departments have repeatedly joined hands in attacking,it still repeated emergence.

The paper emphasize the subjective and objective characters in crime of absorbing public savings,and explains the difference in illegal savings,legal loan and this crime.

The illegal fund-raising nowadays has characteristics of diversity and novelty of the means,the variety of the injury object,the huge amount,and close organized.

Illegal fund-raising refers to the behavior of that,not being authorized by the related legal branches,units or individuals raise the public s fund by issuing stocks,lottery tickets,investing bonds,and so on,and promising to give the investors money,material objects in return for their principal and interest during a certain time limit.