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:

    @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:

    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.

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