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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: 1,969
Registered: 12/4/12
Re: Minimal Hausdorff Topology
Posted: Feb 11, 2013 3:37 AM
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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.









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