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.
♦
For oriented compact n-dimension topological manifold M,
biliear form

is exact,


♦
2. Interpretation
Word := MBoundary of language := pDual language :=
and
Language := 
Word := MBoundary of language := pDual language :=



3. Explanation
Word is compact and has dimension.
Language has dimension.
Language has boundary.
Boundary makes dual language.
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
Distance Theory
Mirror Theory
Guarantee of Language
Tokyo
25 May 2012Sekinan Research Field of Language
25 May 2012Sekinan Research Field of Language
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