Metric Spaces in Calculus

The notions of convergence and continuity are not applicable in advanced mathematics.

The concepts of convergence and continuity are unrelated to the notion of distance.

The arguments concerning convergence and continuity are fundamentally different in one and several variable calculus.

The notions of convergence and continuity can be formulated in terms of distance. (correct)

Develop a theory that is specific to one variable calculus.

Introduce a new concept unrelated to convergence and continuity.

Provide a general theory that covers all mathematical examples. (correct)

Replace the concept of distance with a new notion of convergence.

A set X equipped with a function d of one variable that measures the convergence.

A set X equipped with a function d of two variables that measures the distance between points. (correct)

A set X equipped with a function d of two variables that measures the continuity.

A set X equipped with a function d of three variables.

<p>To develop new notions of convergence and continuity.</p> Signup and view all the answers

<p>New notions of convergence and continuity based on the notion of distance.</p> Signup and view all the answers