Search   Memberlist   Usergroups
 Page 1 of 1 [1 Post]
Author Message
Martin Ziegler
science forum beginner

Joined: 12 Dec 2005
Posts: 2

Posted: Sat Jul 08, 2006 8:17 am    Post subject: function semi-algebraic over real closed sub-field?

Hi. Getting right to the point:

Let F be a real-closed subfield of the reals R.
Let f : [0,1]^n -> R denote a continuous real
function, semi-algebraic (over R), satisfying that
f(x) lies in F for every rational x (i.e. on Q).

Does this imply f to be semi-algebraic over F?

(It does under the additional hypothesis
that f be a rational function: solve the
interpolation problem for (x,f(x)), x in Q )

If it does not,
how about if f is differentiable or analytic?

Thanks for listening
Martin

 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 Page 1 of 1 [1 Post]
 The time now is Fri Sep 21, 2018 9:28 am | All times are GMT
 Jump to: Select a forum-------------------Forum index|___Science and Technology    |___Math    |   |___Research    |   |___num-analysis    |   |___Symbolic    |   |___Combinatorics    |   |___Probability    |   |   |___Prediction    |   |       |   |___Undergraduate    |   |___Recreational    |       |___Physics    |   |___Research    |   |___New Theories    |   |___Acoustics    |   |___Electromagnetics    |   |___Strings    |   |___Particle    |   |___Fusion    |   |___Relativity    |       |___Chem    |   |___Analytical    |   |___Electrochem    |   |   |___Battery    |   |       |   |___Coatings    |       |___Engineering        |___Control        |___Mechanics        |___Chemical

 Topic Author Forum Replies Last Post Similar Topics Units for electric field strength Gavin Electromagnetics 0 Thu Aug 24, 2006 3:00 pm Generating function for Mathieu functions cosmicstring@gmail.com Math 1 Fri Jul 21, 2006 8:39 am Infinitesimal generator of a vector field Julien Santini Math 0 Fri Jul 21, 2006 8:01 am Choice function over finite sets Peter Webb Math 5 Fri Jul 21, 2006 3:28 am Function from Taylor series? Nathan Urban Research 1 Thu Jul 20, 2006 12:48 am