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Brouwer Fixed Point Theorem: Every continuous function from the closed ball B^n= {x∈R^n: abs(x)<1}
to itself has a fixed point.
Is anyone can help me to Prove the Brouwer Fixed point theorem for n = 1 using the fact: there is no retraction from the closed interval [-1,1] onto
the two point set {-1,1}.
also Assume that there is no retraction from the closed ballB^n= {x∈R^n: abs(x)<1} onto the sphere
S^n-1= {x∈R^n: abs(x)=1} Prove the
Brouwer Fixed Point Theorem.
Thanks
to itself has a fixed point.
Is anyone can help me to Prove the Brouwer Fixed point theorem for n = 1 using the fact: there is no retraction from the closed interval [-1,1] onto
the two point set {-1,1}.
also Assume that there is no retraction from the closed ballB^n= {x∈R^n: abs(x)<1} onto the sphere
S^n-1= {x∈R^n: abs(x)=1} Prove the
Brouwer Fixed Point Theorem.
Thanks