Fixed point
Not what you're looking for?
Hello, can someone please help me with the following problem:
Let f : [a, b] -> [a, b] be a homeomorphism such that f (a) = b and f (b) = a. Prove that f has exactly one fixed point.
Purchase this Solution
Solution Summary
This solution provides an example of proving a homeomorphism has exactly one fixed point.
Solution Preview
Proof:
Since f is a homeomorphism, then f has inverse g = f^(-1). Moreover, both f and g are continuous functions.
First, I claim that f has one fixed point.
We consider the function h(x) = f(x) - x. Since f is continuous, then h is also continuous. From the condition, we ...
Purchase this Solution
Free BrainMass Quizzes
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.
Exponential Expressions
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.