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Homeomorphism

Definitions:homeomorphism: h:j->k is a homeomorphism if it is continuous, one-to-one, onto, and also its inverse is continuous.fixed point: a fixed point x of a function f is a point such that f(x) = xattractive fixed point: a fixed point p of a function f such that for all numbers x in the neighborhood of p we have the limit as n->infinity of f^n(x) ~ p (f^n means f applied to itself n times. so f^3(2) = f(f(f(2))) )Suppose f and g are conjugate to one another (that there exists a homeomorphism h such that h(f(x)) = g(h(x)).if p is an attractive fixed point of f, show that h(p) is an attractive fixed point of g.

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