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Topic: Nhood Space
Replies: 24   Last Post: Jul 3, 2013 10:43 PM

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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: Nhood Space
Posted: Jun 30, 2013 11:09 AM
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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

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