Category Archives: Baer-Specker group

Infinite Commutativity (Part I)

Posted on August 2, 2020 by Jeremy Brazas

The Eckmann-Hilton Principle is a classical argument in algebraic topology/algebra. This argument allows you to conclude that an operation which may be expressed in two different ways (imagine that it may be applied both horizontally and vertically when written) is … Continue reading →

Posted in Baer-Specker group, Homotopy theory, Infinite Group Theory, Infinite products | Tagged , , , , , , | 1 Comment

The Baer-Specker Group

Posted on July 2, 2014 by Jeremy Brazas

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 Uncountability of the Harmonic Archipelago Group

Posted on May 23, 2014 by Jeremy Brazas

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 →

Posted in Baer-Specker group, Fundamental group, harmonic archipelago | Tagged , , , , , , , | 1 Comment