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Apr 22, 2023 at 23:08 comment added user127776 Sorry for getting back to this after a long time, I came across something that always thought it is trivial but then realized it isn't. Why infinite symmetric product of a connected $H$-space is a ring space? Ring space I assume you mean there is a smash product (which turns homotopy groups into a ring). But I don't see that. I'm aware that pairing of the points on the symmetric product and summing them using the $H$-space structure gives a new pairing but it doesn't give a smash pairing.
Jul 10, 2022 at 16:18 vote accept user127776
Jul 10, 2022 at 13:41 history edited Tom Goodwillie CC BY-SA 4.0
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Jul 10, 2022 at 13:23 history answered Tom Goodwillie CC BY-SA 4.0