Distance Theory Algebraically Supplemented
Note 2
Polydisk
Bridge between Ring and Brane
1
For algebraic approach toward language, analytic space is prepared
Polydisk Dn that is useful* to identification of some different figures is defined by the following.
Dn = { ( x1, …, xn ) ∈ For all i, xi < 1 }
2
Dn has real topology that is stronger than Zariski topology.
On real topology, refer to the next.
On Zariski topology, refer to the next.
Algebraic Linguistics / Linguistic Note 13 Zariski Topology / Tokyo August 24, 2007
3
Dn has structure sheaf OhDn that has complex analytic function.
On sheaf and structure sheaf, refer to the next.
4
Finite complex analytic function h1, …, hm ∈ ( Dn, OhDn )
5
Sheaf of ideal I = ( h1, …, hm ) OhDn
On ideal, refer to the next.
6
Subset M = V ( I ) = { P ∈ Dn ; All of j, hj ( P ) = 0 }
7
Sheaf OhM = OhDn / I
8
Local ringed space ( M, OhM ) is the model of complex analytic space.
On local ringed space, refer to the next.
On complex analytic space, refer to the next.
Algebraic Linguistics / Linguistic Note 9 Homomorphism / Tokyo July 28, 2007
9
Neighborhood ( U, OhM | U ) is isomorphism of the model.
On isomorphism, refer to the next.
[Note]
*Usefulness of polydisk will be developed at Distance Theory Algebraically Supplemented Brane Simplified Model on extension of circle’s identification as line segment.
On circle, refer to the next.
Algebraic Linguistics / Linguistic Note 4 Grassmann Manifold / Tokyo July 21, 2007
Tokyo October 31, 2007
Sekinan Research Field of Language
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