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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A series is called divergent if it is not convergent in the usual strong senses of pointwise or, sometimes, uniform convergence.
In asymptotic analysis, and in physics, especially in perturbative QFT etc., often a divergent series is still a very useful concept if regarded as an asymptotic series, as a sum of some such series can be defined in various weaker senses, like Borel summability.
Last revised on November 3, 2022 at 20:02:34. See the history of this page for a list of all contributions to it.