Dual Language Duality of Language

Dual 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 := MBoundary of language := pDual 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 2012Sekinan Research Field of Language