Talk:Initial Topology with respect to Mapping equals Set of Preimages

General point about topology proofs:

I wonder, instead of just referring to the axioms by their numbers, we refer to them by their content. Numerical indices for axiom schemas are inconsistent throughout the literature, and "proof of 1, proof of 2, proof of 3" is as un-insightful as you can get. Besides, LaTeX in section headings looks non-optimal. --prime mover (talk) 22:11, 9 November 2012 (UTC)

Good point. Short descriptions of axioms may be difficult, though. --Lord_Farin (talk) 22:17, 9 November 2012 (UTC)

Here is an example: Pseudometric induces Topology, which, yes, does use numbers as well, but also uses the definition of the axiom in question. Worthy paradigm? --prime mover (talk) 22:27, 9 November 2012 (UTC)

For topologies, that works for me. Other systems need naming on an individual basis. --Lord_Farin (talk) 22:34, 9 November 2012 (UTC)

And it may well be that there is an adequately compact wording that encapsulates the broad definition of the axiom. Bridge our cum when we cross to it. --prime mover (talk) 22:38, 9 November 2012 (UTC)