
Re: Nhood Space
Posted:
Jun 30, 2013 11:09 AM


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)
?
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne

