Answer to Question #170330 in Real Analysis for Prathibha Rose

Question

Let D is a subset of R² ,(x₀,y₀) element of D and let f: D to R be any function, prove that the following are equivalent.

1. f is continuous at (x₀,y₀).

2. For every epsilon > 0 ,there is a delta >0 such that |f(x,y) -f(x_0,y₀)| epsilon for all (x,y) element. Of D union S_delta (x_0,y₀)

3. For every open subset V of R containing f(x_0,y₀) there is an open subset U of R² contain (x₀,y₀) such that f(U union D) subset of V

Answer 1

Dear Prathibha Rose, your question requires a lot of work, which neither of our experts is ready to perform for free. We advise you to convert it to a fully qualified order and we will try to help you. Please click the link below to proceed: Submit order