Encyclopedia > Continuity property

  Article Content

Continuity property

THEOREM: Suppose that f : [a , b] -> R is continuous on the closed bounded interval [a , b]. Then the image f([a , b]) is also a closed bounded interval.

This theorem contains three assertions:
(i) The image set is an interval. This is the Intermediate Value Theorem.
(ii) This interval is bounded, so that f is bounded.
(iii) This bounded interval is closed, so that f attains both its bounds.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
UU

... University[?] This is a disambiguation page; that is, one that just points to other pages that might otherwise have the same name. If you followed a link here, you ...

 
 
 
This page was created in 41.7 ms