Characteristic function proof
Not what you're looking for?
Let A be a subset of R^n. Show that the characteristic function Xa is continuous on the interior of A and on the interior of its complement A' but is discontinuous on the boundary ∂A = A (bar)∩A' (bar)
Purchase this Solution
Solution Summary
This provides an example of proving continuity and discontinuity of a characteristic function.
Solution Preview
Let f: = chi_A, the characteristic function of A, with codomain {0, 1} equipped with the discrete topology.
Now, recall that a function f : X -> Y is continuous at a point x of X if, for all open V in Y, there is ...
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Multiplying Complex Numbers
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.