Linguistic Note
1
Loop Space
Space X has base point p.
p ∈ X
Unit interval I [0, 1]
Direct product In I×…×I
Continuous mapping α : In → 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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