Talk:Existence and Uniqueness of Generated Topology

This could be cast in the language of Definition:Magma of Sets. But I may be the only soul on this planet understanding what is meant with that definition... --Lord_Farin (talk) 17:24, 28 September 2012 (UTC)

Proofs of Existence

If there is another proof of the existence the generated topology, both those should be placed on one page called "Existence of Generated Topology" using the same technique as is used for multiple proofs. Then the existence proof can be referenced on this page by a link. For symmetry, uniqueness could then be proved in a page called "Uniqueness of Generated Topology". --prime mover (talk) 19:13, 28 September 2012 (UTC)

Should the other proof just be "Follows from the argument in Equivalence of Definitions of Topology Generated by Synthetic Sub-Basis"? --abcxyz (talk) 19:58, 28 September 2012 (UTC)

I'm not a fan of "... from the argument in ..." sort of sentences, it's too vague. If there's an argument that establishes a truth, extract that argument and put it in a page, then link to it. That's how ProofWiki works. --prime mover (talk) 22:28, 28 September 2012 (UTC)

Okay, so how about taking the argument in Equivalence of Definitions of Topology Generated by Synthetic Sub-Basis, except the last line, and put it in to "Existence of Generated Topology/Proof 2", and then replace Equivalence of Definitions of Topology Generated by Synthetic Sub-Basis with something like:

Let $X$ be a set... [blah blah blah]

[conditions $\left({1}\right)$ and $\left({2}\right)$]

In "Existence of Generated Topology/Proof 2", it is shown that $\tau \left({\mathcal G}\right)$ satisfies conditions $\left({1}\right)$ and $\left({2}\right)$.

It follows that $\tau \left({\mathcal G}\right)$ is the unique topology on $X$ satisfying conditions $\left({1}\right)$ and $\left({2}\right)$.

I'm finding this a little tricky here. Any comments? --abcxyz (talk) 23:01, 28 September 2012 (UTC)