Friday, 1 May 2015

Linguistic Note 1 Loop Space


Linguistic Note

1

Loop Space


   TANAKA Akio

Space X has base point p.
p  X
Unit interval I     [0, 1]
Direct product In      I××I
Continuous mapping    α : I X
Boundary of In    δIn
δIn 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>
<On connection>

Tokyo July 19, 2007

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