Tag Archives: earring group

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

Posted in earring space, Free groups, Fundamental group, Inverse Limit, Shape homotopy group, Shape theory, Tree | Tagged , , , , , | 8 Comments

The Baer-Specker Group

One of the infinite abelian groups that is important to infinite abelian group theory and which has shown up naturally in previous posts on infinitary fundamental groups is the Baer-Specker group, often just called the Specker group. This post isn’t … Continue reading

Posted in Baer-Specker group, earring group, earring space, Free abelian groups, Free groups, Group homomorphisms, Infinite Group Theory | Tagged , , , , , , , | 8 Comments

The Harmonic Archipelago Group is not Free

In recent posts, I’ve been writing about the behavior of fundamental groups of the most fundamental “wild” spaces. We did a decent amount of work in a two-part post to convince ourselves that the fundamental group of the earring space … Continue reading

Posted in earring group, earring space, Free groups, Fundamental group, Group homomorphisms, harmonic archipelago | Tagged , , , , , , , , | 2 Comments