Talk:Open Ball is Open Set/Metric Space

The reason why I didn't do this is because the proof for pseudometric spaces is character-for-character identical. Metric Space Axiom $(\text M 4)$ is not used. Caliburn (talk) 22:21, 30 July 2023 (UTC)

I think you can use the above argument as a proof for the pseudometric version, though the other direction is more obvious. --Usagiop (talk) 22:52, 30 July 2023 (UTC)

Same with Pseudometric Space is First-Countable. I thought it would be a better solution to switch the results over to pseudometric and redirect. Caliburn (talk) 22:28, 30 July 2023 (UTC)

I understand your motives but I disagree with your actions.

It is to keep $\mathsf{Pr} \infty \mathsf{fWiki}$ accessible for those still at undergrad level. --prime mover (talk) 05:22, 31 July 2023 (UTC)

I understand this when we're talking about say, sequences vs nets (even where the proofs may be extremely similar) or where the presentation is changed. But since the proof of these statements doesn't use Metric Space Axiom $(\text M 4)$ anywhere, the proof is exactly the same and it's a matter of copy and pasting and changing metric to pseudometric and this just seems a bit awkward. Equally I'd have no problem swapping norm for seminorm where Norm Axiom $\text N 1$: Positive Definiteness is not used. Caliburn (talk) 09:40, 31 July 2023 (UTC)

For a start the cited references talk about metric spaces, not pseudometric spaces.

For another thing, pseudometrics are niche.

Hence this way is better. --prime mover (talk) 16:17, 31 July 2023 (UTC)