On 2/11/2013 2:08 AM, William Elliot wrote: > On Mon, 11 Feb 2013, fom wrote: > >> I am wondering about diagram for >> example 100, Minimal Hausdorff Topology. > > From what book? > >> The "special" basis neighborhoods in >> the diagram do not seem to coincide >> with the defining conditions. >> >> The second coordinate has j>n for that >> n indexing the basis neighborhood, >> but the diagram seems to indicate j<n. > > It does not. > >> Also, if I am correct about the error >> in the diagram, then should not the >> inequality be changed to j>=n so that >> there is a basis neighborhood associated >> with the first row of the diagram as >> with every other row? >> > No, it makes no difference if it's j >= n or j > n. > >> I am probably just misreading the >> definition. But it has me confused. >> > It takes some study to understand. > > There are orders, that of A and that of Z+. > The order for Z+ begins at the bottom with 1 > and goes to the top. Notice how at the top > the rows of dots are closer that at the bottom > indicating a two dimensional dot, dot, dot. > for the rows. >
Thanks. I simply inverted the order for Z+
Now it makes sense.
If you want to see how I am trying to understand how to use it, open the post on "distinguishability"
The post is way too long, but the attempted application of the topology is at the very end.