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 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.