**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

…

…

Every rational function on the real numbers is a pointwise continuous function on its domain of definition.

This follows directly from the fact that real polynomial functions are pointwise continuous

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

Last revised on May 27, 2022 at 23:16:34. See the history of this page for a list of all contributions to it.