1 Language is given by homology group in topological space.
Homology group is given by module’s chain complex.
{Ck}k=0n, {∂k } k=1n
Ck is module.
∂k: Ck → Ck—1 is homomorphism.
∂k-1o∂k = 0 It is meant that set’s boundary’s boundary becomes null set.
2 Meaning is divided by boundary.
3 Word is given by simplex.
4 Simplex has m+1 vertex and m-dimension. It is called m-simplex.
5 Simplex has orientation that is given by permutation.
6 Orientation gives sentence to vector that consists of words.
7 Vector’s element is given by simplex’s vertex.
8 Sentence is given by simplicial complex.
9 Language is given by polyhedron that consists of union of all simplexes.
10 Polyhedron has triangulation.
11 Sphere’s triangulation is given tetrahedron by homeomorphism.
12 Riemann sphere obtains information from Gauss plane.
Refer to the following papers’ group.
13 Minimum model of Symmetry Flow Language is testified by tetrahedron being led from polyhedron’s triangulation.
Tokyo May 17, 2007
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