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>

```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

```

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