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.research

Topic: Cofinal
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
William Elliot

Posts: 248
Registered: 10/7/08
Cofinal
Posted: Oct 25, 2011 6:00 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

Within a (partial) order A set A is cofinal to B when
A subset B and for all b in B, there's some a in A with b <= a.

Defining the lower set of A,
down A = { x | some a in A with x <= a },

the definition can be rewritten as
A subset B subset down A

which is equivalent to
A subset B and down B = down A.

Has the notion of cofinal been extended beyond subsets?
Can two sets A and B for which
down A = down B
or equivalently
A subset down B and B subset down A
that is
for all a in A, some b in B with a <= b and
for all b in B, some a in A with b <= a
be consider cofinal.

For example, are the sets
A = { 1 - 1/2n | n in N }
and
B = { 1 - 1/(2n-1) | n in N }
considered cofinal?

Within complete orders, cofinal would be equivalent
to having the same supremum.




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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.