Re: Re: Searching for a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg70862] Re: [mg70854] Re: Searching for a function*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Mon, 30 Oct 2006 05:32:25 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <ehv8vp$g6f$1@smc.vnet.net> <200610290340.XAA08628@smc.vnet.net>*Reply-to*: murray at math.umass.edu

As I said in my earlier response, you can always use a CONSTANT function from a nonempty set A to a nonempty set B. And a constant function will be continuous no matter what the topologies on A and B. Moreover, if your problem is "constructing" such a function, then at least when B is defined by means of equalities and inequalities, you could use FindInstance to pick some element of B to use as the constant value. Perhaps you've still not asked the question you really are trying to ask. Bonny Banerjee wrote: > I am looking for continuous functions only from set A to set B. Sorry for > not making it clear. > > --Bonny. > > > > > "Bonny Banerjee" <banerjee.28 at osu.edu> wrote in message > news:ehv8vp$g6f$1 at smc.vnet.net... >> Is it possible for Mathematica to solve this problem: >> >> Given sets A and B, does there exist a function from A to B? If yes, what >> is >> the function? >> >> >> Here is an example: >> >> Let, A = {x such that 0<x<11 and Mod[x,2]==0} >> >> B = {y such that 0<y<11 and Mod[y+1,2]==0} >> >> Then, there exists a function from A to B >> >> y = x - 1 >> >> >> Thus, is there a way to specify arbitrary sets A, B, and use Mathematica >> to >> figure out whether there exits a function from A to B or not? >> >> Thanks, >> Bonny. >> >> > > > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Re: Searching for a function***From:*"Bonny Banerjee" <banerjee.28@osu.edu>