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Adam P. Goucher
@apgox
To add to
@QiaochuYuan
's list: The empty space is not contractible, but its loop space is. (See ncatlab.org/nlab/show/homo together with the discussion in the HoTT book which mentions that the loop space of an n-type is an (n-1)-type.)
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QC (in Berlin 7/29-??? w/ COVID 😷)
@QiaochuYuan
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6. the empty graph is disconnected, and so is the empty topological space, for the same reason that 1 isn't a prime number
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QC (in Berlin 7/29-??? w/ COVID 😷)
@QiaochuYuan
whoa this might be too spicy a take for me. as far as i can see the free loop space of the empty space is empty and it doesn't have a based loop space the empty space is the unique (-2)-type or something right? and there aren't any (-3)-types?
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