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Category Archives: General topology
Topologized Fundamental Groups: The Quotient Topology Part 1
Next up for topologies on the fundamental group is what I’d consider the most “natural” one. It’s almost certainly the topology you’d most often get if you asked random topologists on the street to construct one for you. This is … Continue reading
Posted in Algebraic Topology, compactopen topology, Fundamental group, Quasitopological groups, quotient topology, Topological groups, Uncategorized
Tagged compactopen topology, fundamental group, quasitopological fundamental group, quotient map, quotient topology, universal property of quotient maps
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Homotopically Reduced Paths (Part III)
In this last post about reduced paths, I’m going to work through the details of one of the most useful results in wild topology. Writing this post helped me work out my own way of proving this result and hopefully … Continue reading
Shape injectivity of the earring space (Part II)
This is the sequel to Shape injectivity of the earring space (Part I) We’re on our way to proving the canonical homomorphism from the earring group to the inverse limit of free groups is injective. Part I was mostly dedicated … Continue reading