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

Tokyo
25 May 2012
Sekinan Research Field of Language