One of my little dreams is to make and give a workshop about topology for artists, walkers and outher outsiders. It might be called: The topological toolkit. What you didn't know about spaces. Or maybe: Topology as philosophy of space. These are preliminary notes: YouTube topology, Styles of topology, Spaces and maps, Translation, Words in linguistic space, Workshop contents sketch, Workshop content sketch 2. I try to post small updates often, to keep myself working on this.
The Antoine wild sphere - mapping a sphere to the Cantor dis-continuum. This has something to do with the Antoine necklace, another wild object.
The Alexander wild sphere - as an example of a pathological object.theorem.
Sierpinsky carpet, containing both the Knaster bucket handle and the Warsaw circle.
Also found this:
https://blogs.scientificamerican.com/roots-of-unity/a-few-of-my-favorite-spaces-antoines-necklace/ - antoine necklace is a cantor set
http://www.carliner-remes.com/jacob/math/project/ - geometric toplogy
https://people.math.osu.edu/fiedorowicz.1/math655/ - geometric topology
https://jeremykun.com/2012/08/26/metric-spaces-a-primer/ - metric spaces
https://www.quora.com/How-can-I-show-that-the-taxicab-metric-space-and-the-standard-Euclidean-2-space-induce-the-same-topological-space - metric space and toplogy