Rough sketch of theories of retracts

This mathematical note presents a rough sketch of the theory of retracts, collecting main results and relevant references for future use. It covers AR, ANR, AE, and ANE; basic properties of retracts and extensors; products, unions, contractibility, and homotopy; extension and embedding theorems; and Euclidean neighborhood retracts. Some sections are marked as under construction.

This record preserves the 24-page note dated June 23, 2026, available on the author’s Mathematical Memos/Notes page: https://yoshito-ishiki-math.github.io/notes.html. Original PDF: https://yoshito-ishiki-math.github.io/memosandnotes/anrane.pdf.