fom
Posts:
1,039
Registered:
12/4/12
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Re: Minimal Hausdorff Topology
Posted:
Feb 11, 2013 2:36 PM
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On 2/11/2013 3:28 AM, William Elliot wrote:
> On Mon, 11 Feb 2013, fom wrote:
>> The post is way too long, but the attempted application of the topology
>> is at the very end.
>
> Yes, way to long, detailed, rambling and pointless.
>
I am sorry you feel that way.
I see you asking set-theoretic questions occasionally.
Are you aware that the axiom of determinacy is
characterized in terms of two-person games?
That post considered the construction of the
real numbers using Dedekind cuts.
Toward the end of that post, for the purposes
of constructing that topology, I broke up the
state tables and re-interpreted the situation
in terms of questions and determinations. That
is very close to a two-person game.
I do not know whether or not that analysis can
be "made pretty". And, I do not know if it can
be made more relevant to the game-theoretic
descriptions.
I doubt, however, that you can find any analysis
of the real numbers that even hints at an explanation
for the determinacy axioms in the context of any
one of their classical definitions.
But, again, thank you for your help. It is
greatly appreciated.
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