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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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 fom Posts: 1,968 Registered: 12/4/12
Re: Minimal Hausdorff Topology
Posted: Feb 11, 2013 3:37 AM

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.

Date Subject Author
2/11/13 fom
2/11/13 William Elliot
2/11/13 fom
2/11/13 William Elliot
2/11/13 fom
2/11/13 fom
2/14/13 Shmuel (Seymour J.) Metz
2/14/13 fom
2/14/13 fom
2/15/13 Shmuel (Seymour J.) Metz