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Category Archives: Shape theory
Shape injectivity of the earring space (Part II)
This is the sequel to Shape injectivity of the earring space (Part I) We’re on our way to proving the canonical homomorphism from the earring group to the inverse limit of free groups is injective. Part I was mostly dedicated … Continue reading
Shape injectivity of the earring space (Part I)
One of my posts where I did some substantial handwaving is my original post on the fundamental group of the earring space. I wrote about how to understand and work with this group, but I never gave a proof of … Continue reading
The Cech Expansion: nerves of open covers
The Whitehead theorem in homotopy theory basically says that to fully understand the homotopy type of a CWcomplex one only needs to know about the homotopy groups (really, the weak homotopy type). It is very easy to produce spaces to … Continue reading