
Re: Nhood Space
Posted:
Jul 1, 2013 3:58 AM


fom wrote: > On 6/30/2013 10:09 AM, Peter Percival wrote: >> William Elliot wrote: >>> (S,<<) is a nhood space when << is a binary relation for P(S) and >>> for all A,B,C subset S >>> empty set << A << S >>> A << B implies A subset B >>> A << B implies S\B << S\A >>> A << B/\C iff A << B and A << C >> >> >> Is this the same as neighbourhood space defined as follows. >> >> (S, N), S a set, N a map S > PPS (P for power set) and >> >> i) x in S => N(x) =/= 0 >> >> ii) x in S, M in N(x) => x in M >> >> iii) x in S, M in N(x) => (L superset M => L in N(x) >> >> iv) x in S, L, M in N(x) => L intersect M in N(x) >> >> v) x in S, M in N(x) => exists L in N(x) s.t. >> L subset M and, forall y in L, L in N(y) >> >> ? >> >> > > > These are proximity neighborhoods. In the induced > topology they correspond with the usual neighborhood > system which I believe you have described here.
Thank you. I'd been wondering!
> Otherwise not. > > http://en.wikipedia.org/wiki/Proximity_space > >
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne

