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Re: Topology

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16249] Re: Topology
  • From: Trifonov at my-dejanews.com
  • Date: Fri, 5 Mar 1999 00:41:13 -0500
  • Organization: Deja News - The Leader in Internet Discussion
  • References: <7bg21q$5m3@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <7bg21q$5m3 at smc.vnet.net>,
  Vesa-Matti Sarenius <sarenius at student.oulu.fi> wrote:
> 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
>
It's easy:
propertyOne[t_,s_]:=MemberQ[t,{}]&&MemberQ[t,s];
TopologyQIntersections[t_]:=And@@(MemberQ[t, #]&/@
Union[Union/@Flatten[Table[Intersection[t[[i]],t[[j]]],
{i, Length[t]}, {j,i}],1]]);
TopologyQUnions[t_]:=And@@(MemberQ[t, #]&/@
Union[Union/@Flatten[Table[Join[t[[i]],t[[j]]],
{i, Length[t]}, {j,i}],1]]);

Note: it is sufficient to verify all properties for pairs of elements only,
because the set is finite.

Cheers,
Evgeni Trifonov,
Institute of Applied Mathematics,
Vladivostok, Russia.

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