Re: Topology
- To: mathgroup at smc.vnet.net
- Subject: [mg16201] Re: Topology
- From: "Allan Hayes" <hay at haystack.demon.co.uk>
- Date: Fri, 5 Mar 1999 00:40:38 -0500
- References: <7bg21q$5m3@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Vesa-Matti Sarenius wrote in message <7bg21q$5m3 at smc.vnet.net>... >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. * * * * * * > After <<DiscreteMath`Combinatorica` Complement[ Apply[Union, KSubsets[T1, k], {1} ] ,T1 ] will give {} iff the unions of k subsets of T1 are elements of T1 We can similarly test for intersections. This is probably inefficient - you may get some ideas from the other functions of the package, and from their code. Allan