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Tweets by jtbrazas-

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# Category Archives: Free groups

## Topologized Fundamental Groups: The Quotient Topology Part 3 (Why isn’t it always a topological group?)

In Part 1, I mentioned that one of the surprising things about the natural quotient topology on the fundamental group is that the resulting group with topology often fails to be a topological group. In fact, I’d say it’s usually … Continue reading

Posted in compact-open topology, earring group, Free groups, Fundamental group, quotient topology, topological fundamental group, Topological groups, Uncategorized
Tagged commutator, Frechet-Uryshon Fan, free group, infinite earring group, infinite earring space, locally free group, non-locally compact space, quasitopological group, quotient space, sequential space, topological group
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## 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 hand-waving 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