This entry is about conditional convergence of series in real analysis and functional analysis. For conditional convergence of spectral sequences in homological algebra and stable homotopy theory, see conditional convergence of spectral sequences.
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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In real analysis, given a sequence in the real numbers, the series is conditionally convergent if the sequence of partial sums is a Cauchy sequence, but the sequence of partial sums of the series is not Cauchy.
In functional analysis, given a sequence in a Banach space , the series is conditionally convergent if the sequence of partial sums is a Cauchy sequence in , but the sequence of partial sums of the series is not Cauchy in the real numbers.
Last revised on January 4, 2023 at 19:08:25. See the history of this page for a list of all contributions to it.