1 Language is represented by sentence.
2 Sentence is expressed by plane, pillar and torus.
3 Language is represented by torus.
4 Torus consists of one torus or over one toruses.
5 Torus that has over one toruses is called nested torus.
6 Torus that has one torus is called unit torus.
7 Nested torus has multi-time dimensions. Its details are treated by the other papers.
Refer to the following papers.
Nested Torus Theory Nested Torus Theory For PONTLYAGIN Tokyo May 27, 2006
Topological Semantics Definition Tokyo June 5, 2006
8 Unit torus has one sentence.
9 Sentence has lattice. Its details are treated by the other papers.
Refer to the following papers.
Quantum Semantics Lattice Tokyo May 15, 2006-May 28, 2006
Quantum Semantics Lineation Lattice Plane Pillar Tokyo May 24, 2006-May 28, 2006
Also refer to the next paper.
Solid Trace Theory Superlattice Tokyo May 3, 2006
10 Sentences are expressed by toruses.
11 Torus can be cut at start-ending position of sentence. The shape goes back to pillar.
The notion is similar to MAC LANE’s domain. The details will be seen by the other papers.
12 Torus can be adhered.
The notion is similar to MAC LANE’s codomain.
13 Plane, pillar and torus are equivalent.
14 Cut toruses are connected each other.
15 Connected toruses become torus chain.
16 Torus chains have three types.
Lineation type (L type) Toruses form a line.
Ring type (R type) First torus connects last torus.
Hang type (H type) One torus hangs some toruses.
17 Three types of torus chain are recognized to topological viewpoint.
18 Language is expressed by torus chain.
Simple sentence is expressed by a torus.
Compound sentence is expressed by ring type toruses. The situation is related with language’s finiteness. See D 22 in the following paper.
Topological Semantics Definition Tokyo June 5, 2006
Complex sentence is expressed by hang type toruses.
Unfinished sentence is expressed by lineation type toruses.
19 Torus chain has strong structure for its topological situation.
20 A torus, ring type toruses and hang type toruses belong to finite group.
21 Lineation type toruses belong to infinite group.
22 Three types of toruses are considered by group. The details are treated by the other papers.
Tokyo June 10, 2006
Sekinan Research Field of Language
www.sekinan.or
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