Tag Archives: semilocally simply connected

Topologized Fundamental Groups: The Quotient Topology Part 2 (Discreteness)

In Part 1, I described the construction of , the fundamental group equipped with the quotient topology and some of the drama around failing to always be a topological group. In this second post, I plan to connect back to … Continue reading

Posted in Fundamental group, Uncategorized | Tagged , , , | 4 Comments

Testing the limits of Eda’s Theorem

With everything going on, it’s been a bit tough to find time to post about the things I’d like to. I’ve promised posts about topological homotopy groups for a while but I want to do those right, so it may … Continue reading

Posted in earring group, earring space, Fundamental group, Homotopy theory | Tagged , , , | Leave a comment

Homotopically Hausdorff Spaces (Part I)

In previous posts, I wrote about the harmonic archipelago  (see also here and here): as well as the Griffiths Twin Cone . One special feature of these 2-dimensional spaces is that any loop either of these spaces can be deformed to lie … Continue reading

Posted in Covering Space Theory, Fundamental group, Griffiths twin cone, harmonic archipelago, Homotopy theory, Uncategorized | Tagged , , , | 3 Comments