Category Archives: Homotopy theory

Higher Dimensional Earrings

Posted on November 23, 2019 by Jeremy Brazas

The (1-dimensional) earring space is a 1-dimensional Peano continuum (connected, locally path-connected, compact metric space) constructed by adjoining a shrinking sequence of circles at a single point. The importance of stems from the fact that this is the prototypical space … Continue reading →

Posted in Homotopy theory | Tagged , | 1 Comment

Homotopically Hausdorff Spaces (Part II)

Posted on March 18, 2017 by Jeremy Brazas

In my post homotopically Hausdorff spaces (Part I), I wrote about the property which describes the existence of loops that can be deformed into arbitrarily small neighborhoods but which are not actually null-homotopic, i.e. can’t be deformed all the way back … Continue reading →

Posted in Algebraic Topology, earring space, Fundamental group, Group homomorphisms, harmonic archipelago, homotopically Hausdorff, Homotopy theory | Tagged , , , | 2 Comments

Homotopically Hausdorff Spaces (Part I)

Posted on March 14, 2017 by Jeremy Brazas

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