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

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William Elliot

Posts: 2,637
Registered: 1/8/12
Minimal Hausdorff Topology
Posted: Feb 11, 2013 3:08 AM
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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.

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