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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
Infinite Commutativity (Part I)
The EckmannHilton 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
What is an infinite word?
In this post, we’ll explore the idea of noncommutative 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