メモとノート

Mathematical Memos/Notes

1. A cheatsheet on non-Archimedean analogues in metric geometry (PDF)/ source files zip
   Explanation of non-Archimedean analogous theorems in metric geometry with corresponding Archimedean theorems.
2. A memo on paracompactness (PDF)
   The proof that every open covering of a paracompact Hausdorff space has a refinement that is a sigma-discrete and locally finite open covering.
3. Memo: describing perfect maps with pullbacks (PDF)
   A characterization of perfect maps using the universality of pullbacks.
4. Rough sketch of theories of retracts (PDF) / zip files: source
   A rough sketch of theories of retracts, including references on fundamental theorems on retracts.
   DOI: 10.5281/zenodo.22423945 (Version 1.0, 23 June 2026; CC BY 4.0)
   Citation and record details / 引用・登録情報

   Zenodo record (PDF, 24 pages)

   BibTeX:

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   @techreport{Ishiki2026Retracts,
     author      = {Ishiki, Yoshito},
     title       = {Rough sketch of theories of retracts},
     institution = {Zenodo},
     type        = {Mathematical note},
     version     = {1.0},
     year        = {2026},
     date        = {2026-06-23},
     doi         = {10.5281/zenodo.22423945},
     url         = {https://doi.org/10.5281/zenodo.22423945}
   }

   Plain-text citation:

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   Yoshito Ishiki, “Rough sketch of theories of retracts,” mathematical note, version 1.0, Zenodo, 23 June 2026. https://doi.org/10.5281/zenodo.22423945.

   Concept DOI for all versions: 10.5281/zenodo.22423944

   PDF SHA-256 (version 1.0):

   e0f594145f9e7211f621cc4f163dbf08b12afdc142f193984e38481c3eaa040b
5. Dimension theory of separable metrizable spaces (PDF)
   A note on dimension theory of separable metrizable spaces, including theorems and proofs.