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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, 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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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 profinite groups, Lie groups, ordered groups, etc, also arise in many different areas. So it’s natural to ask, can the … Continue reading
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