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I wrote a series of blog posts about persistent homology and topological data analysis for absolute beginners as I was obsessed with it for some time: http://ou
by outlace 6y ago
I wrote a series of blog posts about persistent homology and topological data analysis for absolute beginners as I was obsessed with it for some time: http://outlace.com/TDApart1.html http://outlace.com/TDApart1.html
- flafla2 6y agoThis looks great, thanks!
- 3PS 6y agoJust briefly skimming over your post, a quick correction to the Continuity section: > Definition (Homomorphism) There is a homomorphism (i.e. an equivalence relation) between two topological spaces if there exists a function f:X→Y, where X and Y are topological spaces (X,τX) and (Y,τY) with the following properties This should be "homeomorphism", not "homomorphism". A homomorphism is a structure-preserving map, like a continuous function (in the context of topological spaces) or a linear map (in the context of vector spaces). Homomorphisms are very much one-directional. Homeomorphisms, on the other hand, are specifically equivalences between topological spaces, and are defined as continuous functions with continuous inverses. Edit: finished reading it. I'm impressed by how much you cover in such a short space. Overall it looks good, so thanks for taking the time to write it. Some of these ideas are at a pretty high level of abstractness, so I sympathize with anyone who struggles to get any kind of intuition for them at a first go.
- outlace 6y agoThanks for the correction!