Tag Archives: fundamental group

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, compact-open topology, Fundamental group, Quasitopological groups, quotient topology, Topological groups, Uncategorized | Tagged , , , , , | 1 Comment

How to “topologize” the fundamental group: a primer

The fundamental group, from algebraic topology, is one of the most widely used invariants in mathematics. Topological groups, such as pro-finite groups, Lie groups, ordered groups, etc, also arise in many different areas. So it’s natural to ask, can the … Continue reading

Posted in Algebraic Topology, Fundamental group, Topological groups, Uncategorized | Tagged , , , , | 3 Comments

The Griffiths Twin Cone

This post is about an important wild space which, in many ways, is similar to the harmonic archipelago space that I posted about a few weeks ago. The Griffiths twin cone (or Griffiths space) was first studied by H.B. Griffiths in the 1950’s … Continue reading

Posted in Algebraic Topology, earring space, Fundamental group, Griffiths twin cone | Tagged , , , , , | 6 Comments