The topologist’s world map (2020)
tafc.space
The topologist’s world map (2020)
1–10 of 71 posts
Re: The topologist’s world map (2020)
#2I still find a Spilhaus projection more informative, but this is defo interesting!
Re: The topologist’s world map (2020)
#3This is beautiful, especially with the colors on the top right - though I have a nitpick that it is missing an entire continent (probably because it doesn't show up in a list of countries): Antarctica
Edit: I now realize it's only supposed to show the graph national borders, though on a political world map, Antarctica is still shown. In a topological fashion, it could be added as a white circle around the entire map.
Re: The topologist’s world map (2020)
#4That tiny Canada-Panama striped tail containing the entirety of North and Central America is funny.
Re: The topologist’s world map (2020)
#5The site is currently being hugged to death, so if you find its resources exhausted, try the archived version from a couple of hours back:
http://web.archive.org/web/20221219173909/tafc.space/qna/the...
Re: The topologist’s world map (2020)
#6[deleted]
Re: The topologist’s world map (2020)
#7That tiny Canada-Panama striped tail containing the entirety of North and Central America is funny.
This map tends to give vertex-like countries large areas, and vice-versa.
Re: The topologist’s world map (2020)
#8[deleted]
Re: The topologist’s world map (2020)
#9I still find a Spilhaus projection more informative, but this is defo interesting!
Definitely if you're an oceanographer. Interesting link here [0].
[0] https://storymaps.arcgis.com/stories/756bcae18d304a1eac140f1...
Re: The topologist’s world map (2020)
#10For people who have time to burn being uselessly pedantic, is this a topologist's world map up to homotopy equivalence or homeomorphism?
[edit]
I think I get how to encode a hypergraph as a topological space. Let S be a set consisting of two kinds of points: Nodes and hyperedges. Endow it with a topology whose base consists of singleton sets containing only single nodes, and sets containing a hyperedge together with all the nodes it's connected to. In particular, a hyperedge cannot be in an open set unless it's accompanied by the nodes it's connected to. Observations are: The resulting space is usually not T2 or T1, but is always T0; connectivity of the hypergraph is equivalent to connectivity of the topological space; the Sierpinski space results from using a graph with one node and edge.
I don't know what that accomplishes except validate the intuition that graph theory is somehow connected to topology.