Drexel dragonThe Math ForumDonate to the Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 1,968
Registered: 12/4/12
Re: Nhood Space
Posted: Jun 30, 2013 10:21 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

Otherwise not.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum 1994-2015. All Rights Reserved.