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 a formal precursor to a various notions of a sum of an infinite sequence.
An (ordinary) series whose members are the elements in a given additive group is an ordered pair of a sequence and a sequence of its partial sums .
The most straightforward notion of the sum of a series is the limit of its sequence of partial sums, if this sequence converges, relative to some topology on the space where the members of the sequence belong to. A series that does not converge in this sense is called divergent; sometimes these can also be “summed” by fancier techniques.
Last revised on July 5, 2017 at 05:02:28. See the history of this page for a list of all contributions to it.