Google Groups Home
Help | Sign in
sci.math
+ new post
About this group
Subscribe to this group
This is a Usenet group - learn more
Dedekind-MacNeille completion
Options
There are currently too many topics in this group that display first. To make this topic appear first, remove this option from another topic.
There was an error processing your request. Please try again.
flag
   1 message - Collapse all
The group you are posting to is a Usenet group. Messages posted to this group will make your email address visible to anyone on the Internet.
Your reply message has not been sent.
Your post was successful
William Elliot  
View profile
  More options Oct 6, 4:21 pm
Newsgroups: sci.math
From: William Elliot <ma...@hevanet.remove.com>
Date: Mon, 6 Oct 2008 04:21:05 -0700
Local: Mon, Oct 6 2008 4:21 pm
Subject: Dedekind-MacNeille completion
Reply | Reply to author | Forward | Print | Individual message | Show original | Report this message | Find messages by this author
Let S be an (partially) ordered set.  For A subset S, let
        above A = set of upper bounds of A.
        below A = set of lower bounds of A.

The Dedekind-MacNeille completion of S is
        M = { below above A | A subset S }

If S is a Boolean algebra, then M is a Boolean algebra.

In particular, when A subset S, what set B is there for which

        below above A /\ below above B = {0}
        sup{ below above A, below above B } = S.

Alas it is not S\A.


    Reply    Reply to author    Forward  
You must Sign in before you can post messages.
To post a message you must first join this group.
Please update your nickname on the subscription settings page before posting.
You do not have the permission required to post.
End of messages
« Back to Discussions « Newer topic     Older topic »

Create a group - Google Groups - Google Home - Terms of Service - Privacy Policy
©2008 Google