Question

A function which is uniformly continuous on a dense set

Answer 1

Answer:

Every function that's uniformly continuous on a dense subset has a continuous extension to the whole set. To make this statement precise, let's recall that, for a set A of real numbers, a subset B ⊂ A is said to be dense in A if, for every point a ∈ A, every ε-neighborhood Vε(a) of a contains a point of B.

Answer 2

Answer:

Step-by-step explanation:

Every function that's uniformly continuous on a dense subset has a continuous extension to the whole set. To make this statement precise, let's recall that, for a set A of real numbers, a subset B ⊂ A is said to be dense in A if, for every point a ∈ A, every ε-neighborhood Vε(a) of a contains a point of B.