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Tag Archives: fundamental group
The Uncountability of the Harmonic Archipelago Group
In a previous post, we discussed the fundamental group of the harmonic archipelago in some detail. One item that I skipped earlier is the fact that this group is uncountable. In this post, we’ll see why is uncountable. We’ll use … Continue reading
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 twopart post to convince ourselves that the fundamental group of the earring space … Continue reading
The earring group is not free (Part II)
This post is Part II in an explanation of why the fundamental group of the earring space is not a free group. I’ll be referencing the notation and results that we worked through in Part I. Recall that the earring group is … Continue reading