Duality of Language

Duality of Language

TANAKA Akio

1. Theorem
(Poincaré duality)
For oriented compact n-dimension topological manifold M,
biliear form

is exact,
and become dual space each other.
♦

2. Interpretation
Word := M
Boundary of language := p
Dual language := and
Language :=

3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.

4. References
Distance Theory
Mirror Theory 
Guarantee of Language