Date: Nov 6, 2013 10:38 PM
Author: William Elliot
Subject: Re: Partition of a filter
On Wed, 6 Nov 2013, Victor Porton wrote:

> William Elliot wrote:

> > On Tue, 5 Nov 2013, Victor Porton wrote:

> >> > As for Conjecture 4.153, obviously no,

> >> > a filter cannot be partitioned into ultrafilters because

> >> > all the ultrafilters contain the same top element.

> >> >

> >> > Do you mean this instead?

> >> >

> >> > If F is a filter for S, can F be partitioned

> >> > into ultrafilters for subsets of S?

> >>

> >> I mean that filter can be partitioned into ultrafilters in the REVERSE

> >> order.

> >

> > What does order have to do with it? A partition of a set S, or a

> > collection of sets like filters are, is a pairwise disjoint collection

> > whose union is S.

>

> No, for filters I define it differently. See my book:

>

> http://www.mathematics21.org/algebraic-general-topology.html

Not possible. Where, in the old numbering is the definition?

> (I fact I define it in two different ways, which are not equivalent.)