@Felthry second one looks like a bandaged tongue
@lioness the second one??
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@Felthry third one sorry
@lioness okay that makes more sense
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@lioness it is apparently "closed union with smash product"
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@Felthry …huh.
@lioness we have no idea what that means, you'd probably have to ask a mathematician and then it'd have to be one in a very particular subfield
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@Felthry @lioness wait no I got that wrong
ok you start with the two lines. their product is a plane.
then, you look at the copies of the two lines in the new space. that'd be the coordinate axes.
crunch those down into the origin. what do we get? each of the four quadrants of the plane gets quotiented down into... something. whatever it is, there's four of them, they're all the same shape, and they glue together to each other at the origin.
each one of those, we can make easier to understand by taking the resulting quarter-infinite plane, prying it open again into a full plane - or, if you prefer, folding it around to glue like you're making a party hat
and now we have four of these in a kind of bouquet, so what we have is actually four planes joined exactly at their origins
I think.
@Felthry @lioness a product in the topological sense is, like, dragging one space along another
like, the product of a circle and a line is an infinite cylinder, for example