rational functions are continuous

**analysis** (differential/integral calculus, functional analysis, topology)

metric space, normed vector space

open ball, open subset, neighbourhood

convergence, limit of a sequence

compactness, sequential compactness

continuous metric space valued function on compact metric space is uniformly continuous

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…

Every rational function is a continuous function on its domain of definition.

This follows directly from the fact that polynomial funcitons are continuous?

A proof using epsilontic analysis is spelled out for instance around corollary 3.16 here:

Created on May 7, 2017 at 10:21:08. See the history of this page for a list of all contributions to it.