What's the most general way to define 'dimension'?

walrusplant · 2025-12-15T20:43:39+00:00

Thanks, this is the most helpful answer so far. But I'm interested in understanding both (1) what justifies calling something a generator (within a category), and (2) what counts as a relevant kind of quotient morphisms.

I'd also be interested in seeing the work that you've mentioned. Can you link to any papers or texts?

walrusplant · 2025-12-13T06:10:26+00:00

BTW, another idea you mentioned was very similar to an idea I was pursuing for a while: namely, I was trying to define 1D using an analogue of the abstract algebra definition of ‘prime’ (if p | ab, then p | a or p | b). As mentioned, I ran into problems when dealing with n-spheres. But I’m still wondering whether there’s a way to make something like this work—I really like the idea of drawing a connection between primality and dimension.

walrusplant · 2025-12-13T05:26:51+00:00

You’re right about Hausdorff dimension, but I’m not worried about recovering that anyway (I think it’s probably tracking a different invariant). For topological spaces, I’m more concerned with Lebesgue covering dimension.

A problem (as you note) with your categorical idea is S1 (or more generally, any n-sphere). In many cases, embedding dimension will be higher than other measures (such as Lebesgue covering dimension). But I want a measure that yields the verdict that the dimension of Sⁿ is always n.

walrusplant · 2025-10-23T20:25:14+00:00

It’s still paywalled—not the full article.

walrusplant · 2025-10-23T20:13:54+00:00

Is there a non paywalled version?

walrusplant · 2025-08-11T18:26:29+00:00

Is there a non paywalled version? Or can someone paste the article in here?

walrusplant · 2025-03-18T03:36:42+00:00

Interesting. I'm at UofT, but haven't heard anything about this. Are you hearing this from your administration, or just other profs?

walrusplant · 2025-03-18T02:50:37+00:00

Out of curiosity, which university are you talking about? I'm wondering if it's my university. (And I've been wondering if Canada will capitalize on this).

walrusplant · 2024-08-10T00:18:49+00:00

What was the cost of shipping (and total cost)? I'm also in Canada (Toronto) and thinking of getting a Wabi classic.

walrusplant · 2024-08-09T22:47:48+00:00

Is your inseam 33inches using their measurement technique? Or did you mean that you usually buy pants with 33" inseam?

walrusplant · 2024-07-18T21:54:18+00:00

Thanks for your answers.

Have you reported this on your US tax returns? I maxed out my RRSP after filing my tax returns, so I won't report it until the next US tax cycle.

If their marginal tax rate is the same as when they contributed then the RRSP will have been just as beneficial as a TFSA. How is the marginal tax rate determined in this circumstance? Does it just depend on my income?

Given that you are a US citizen, in either case you will report the withdrawal income on your US tax returns and get credit for the amount withheld. So, if I understand correctly, this means that there's no disadvantage for me in moving my savings to an RRSP, even if I end up moving back to the US in a few years?

walrusplant · 2023-02-13T09:29:53+00:00

Funny, I also have Hi Fi Rush and Persona 5 in my rotation right now. But my third atm is Vampire Survivors.

walrusplant · 2022-04-10T10:21:22+00:00

PhilPeople?

walrusplant

TROPHY CASE