Tag Archives: infinite product

Homotopically Reduced Paths (Part II)

Understanding this post requires reading Part I where I explain what reduced paths are and how we might go about proving they exist. In this second part, I’ll go into detail about how to use Zorn’s lemma to identifying a … Continue reading

Posted in Fundamental groupoid, reduced paths | Tagged , , , , , , , | 1 Comment

Infinite Commutativity (Part I)

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

What is an infinite word?

In this post, we’ll explore the idea of non-commutative infinitary operations on groups, that is, multiplying together infinitely many elements in a group. This idea arises very naturally in “wild” or “infinitary” algebraic topology. In fact, lately, this has been … Continue reading

Posted in Group theory, Infinite Group Theory, Order Theory | Tagged , , , , , , , , | 1 Comment