topología

E_{k} = { x€[0,oo]_{K} : x < a_{1}+...(k)...+a_{k} }

F_{k} = { x€[0,oo]_{K} : a_{1}+...(k)...+a_{k} [< x }

Si x < S_{m} [< a_{1}+...(k)...+a_{k} [< S_{n} ==>

E_{n} = E_{m}[ || ]...(k)...[ || ]E_{n}

E_{m} = E_{m}[ & ]...(k)...[ & ]E_{n}

E_{m} [<< ...(k)... [<< E_{n}

Si S_{m} [< a_{1}+...(k)...+a_{k} [< S_{n} [< x ==>

F_{m} = F_{n}[ || ]...(k)...[ || ]F_{m}

F_{n} = F_{n}[ & ]...(k)...[ & ]F_{m}

F_{n} [<< ...(k)... [<< F_{m}

G_{k} = { x€[0,oo]_{K} : x [< a_{1}+...(k)...+a_{k} }

H_{k} = { x€[0,oo]_{K} : a_{1}+...(k)...+a_{k} < x }

Si x [< S_{m} [< a_{1}+...(k)...+a_{k} [< S_{n} ==>

G_{n} = G_{m}[ || ]...(k)...[ || ]G_{n}

G_{m} = G_{m}[ & ]...(k)...[ & ]G_{n}

G_{m} [<< ...(k)... [<< G_{n}

Si S_{m} [< a_{1}+...(k)...+a_{k} [< S_{n} < x ==>

H_{m} = H_{n}[ || ]...(k)...[ || ]H_{m}

H_{n} = H_{n}[ & ]...(k)...[ & ]H_{m}

H_{n} [<< ...(k)... [<< H_{m}

Homotopía:

[Es][ f(1,0) = g(1,0)+s ] & [Es][ f(0,1) = g(0,1)+s ]

reflexiva

s = f(1,0)+(-1)·g(1,0) & s = f(0,1)+(-1)·g(0,1)

simétrica:

Es defineish: t = (-s)

transitiva:

Es defineish: t = s_{1}+s_{2}

f: { x }x{ y } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = x^{2}+y^{2}

f(0,1) = 1

f(1,0) = 1

f: { x^{2} }x{ y^{2} } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = x+y

f(0,1) = 1

f(1,0) = 1

f: { xy }x{ yx } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = (1/y)^{2}·x^{2}+(1/x)^{2}·y^{2}

f(0,1) = oo^{2}

f(1,0) = oo^{2}

f: { x+y }x{ y+x } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = (x+(-y))^{2}+(y+(-x))^{2}

f(0,1) = 2

f(1,0) = 2

f: { x^{2}+y }x{ y^{2}+x } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = (x+(-y))+(y+(-x))

f(0,1) = 0

f(1,0) = 0

f: { g(x) }x{ g(y) } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = ( g^{o(-1)}(x) )^{2}+( g^{o(-1)}(y) )^{2}

f(0,1) = ( g^{o(-1)}(1) )^{2}+( g^{o(-1)}(0) )^{2}

f(1,0) = ( g^{o(-1)}(0) )^{2}+( g^{o(-1)}(1) )^{2}

f: { g(x)+y }x{ g(y)+x } ---> { x^{2}+y^{2} } & ...

... < x,y > ---> f(x,y) = ( g^{o(-1)}(x+(-y)) )^{2}+( g^{o(-1)}(y+(-x)) )^{2}

f(0,1) = ( g^{o(-1)}(-1) )^{2}+( g^{o(-1)}(1) )^{2}

f(1,0) = ( g^{o(-1)}(1) )^{2}+( g^{o(-1)}(-1) )^{2}