See: Math notebook, Category theory glossary

**Investigation: Relate my concepts with persistent homology, topological data analysis and homotopy type theory.**

- Understand these domains.
- Make a map of key concepts in these domains.
- Relate the univalence axiom (A=B) \simeq (A\simeq B) and the Yoneda lemma.
- Relate persistent homology to the kissing number.

- Relate to my philosophical concepts.
- Study the kinds of equivalences. Associate them to the relationship between level and metalevel.
- Relate spectral sequences, exact sequences and divisions of everything.

- Do calculations with practical examples.
- Make a map of mathematics by studying sets of tags at Math Stack exchange and Math Overflow. Use it to predict (using duality) the location of new theorems and concepts.
- Study ways of identifying new concepts in chess.
- Make a map of deepest values.

**Readings: Topological data analysis**

- Wikipedia: Persistent homology
- Wikipedia: Topological data analysis
- Wikipedia: Spectral sequence
- Edelsbrunner, Harer: Persistent Homology — a Survey.
- Edelsbrunner, Morozov: Persistent Homology: Theory and Practice

**Readings: Homotopy type theory**

- Wikipedia: Homotopy type theory
- Wikipedia: Homotopy
- Wikipedia: Univalent foundations
- Wikipedia: Intuitionistic type theory
- Wikipedia: Type theory

**Ideas**

- What about a reverse approach... where we divide up the space into regions where there are points and where there are not. Consider the largest circles that you can create with no points in it. You can do this by considering the bisecting points on the segments between each pair of points - use these as the centers of your circles. So this will give you a break down into regions. Now do this again allowing a circle to contain one point. (This is perhaps the current case? - for we can use each point as the center of a circle.) Then continue by allowing it to contain 2 points. And so on.

Parsiųstas iš http://www.ms.lt/sodas/Book/KrasauskasKulikauskas

Puslapis paskutinį kartą pakeistas 2019 vasario 15 d., 17:58