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