Topology
- To: mathgroup at smc.vnet.net
- Subject: [mg16183] Topology
- From: Vesa-Matti Sarenius <sarenius at student.oulu.fi>
- Date: Tue, 2 Mar 1999 01:13:22 -0500
- Organization: University of Oulu
- Sender: owner-wri-mathgroup at wolfram.com
Hip!
Anyone done this?
T1 is a topology for a set A if
1. {} and A are in T1 ({} is the empty set.)
2. Any union of members in T1 is in T1
3. Any intersection of finitely many members of T1 is in T1
Then an example:
Let A={a,b,c}
then T1={{},A,{a},{a,b},{c},{a,c}} is a topology for A.
I am trying to do a Mathematica code program to determine for finite
sets (like A above) whether T1 is a topology.
First I did this:
ElementQ[set_,element_]:=
Module[{i=0,t=False},While[i<Length[set],i=i+1;
If[element==set[[i]],t=True,
t=t]];t]
This checks whether some a is a member of T1
T1={{},{a,b,c},{a}}
E.g. ElementQ[T1,{}] gives True.
Now I am desperately trying to do:
-TopologyQIntersections
-TopologyQUnions
two functions which would check the marks 2. and 3. from the definition,
using the help of ElementQ.
I came up with about nothing. So if anyone have done this or can help me
otherwise, please do so.
--
Vesa-Matti Sarenius * - Am I a man or what? - A What!*
mailto:sarenius at paju.oulu.NOSPAMfi* - What? - Yes, that's right! *
Koskitie 47 A6 FIN-90500 OULU * * * * *
http://www.student.oulu.fi/~sarenius * * * * * * * * * * hmmmm! *
Finland, Europe. Tel. +358-8-342236 fax.+358-8-5305045. * * * * * *
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