what is the purpose of some of these weird unicode characters
ⱺ
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today in "Felthry has been reminded of the existence of the character map":
ⱺꝅ⩐ᵺⱴʨ
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@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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@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 I assume the "closed union" is literally that, the closure of the union of two spaces (in some other ambient space)
the smash product is a very basic but slightly weird construction in topology - basically, you product two spaces together and then you look at the copies of the two factor spaces sitting in the product and you slorp them down to the origin point
the smash product of two lines, for instance, is (I think) the union of four open 3-balls plus a point to tie them together
the smash product of two circles is a normal 2-sphere, if one with a *really* fucked up induced metric.
(I assume that the serifs are purely typographical, with no mathematical meaning)
@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.