Linguistic Note 1 Loop Space / July 19, 2007

Linguistic Note

1

Loop Space

　　　TANAKA Akio

Space X has base point p.

p ∈ X

Unit interval I     [0, 1]

Direct product I_n      I×…×I

Continuous mapping    α : I_n → X

Boundary of I_n    δI_n

δI_n has mapping to p.   It is M.

Euclid space Rⁿ⁺¹ has vector that longitude is 1.

All the vectors become set Sⁿ.

Continuous mapping     H : I×I _n → X

H ( 0, t) = α   0≤t≤1/2

H ( 1, t) = β   1/2≤t≤1

α and β are loops.

α. β becomes composite of loops.

[Note]

The composite of loops may be helpful to the connection of words in language.

[References]

<On loop>

Symmetry Flow Language     Meaning Variation and Time Shift in Word as Homotopy     Tokyo May 17, 2007

<On connection>

Language and Spacetime     Construction of Spacetime     Especially on Transformation with Boundary for Dimensions     Tokyo April 24, 2007

Symmetry Flow Language 2     Boundary, Deformation and Torus as Language     Tokyo May 19, 2007

Cell Theory     Conifold as Word     Tokyo June 9, 2007

Tokyo July 19, 2007

Sekinan Research Field of Language