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Topic:
help with misprint (?) Counterexamples in topology
Replies:
9
Last Post:
Feb 15, 2013 8:54 AM




Minimal Hausdorff Topology
Posted:
Feb 11, 2013 3:08 AM


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.



