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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By a sequential preconvergence space we shall mean the most general kind of topological space where the notion of convergence and limit for sequences makes sense. The possibly more evident term “sequential convergence space” for this notion is already taken to mean a synonym of subsequential space, but that definition is not the most general definition for which the notions of convergence and limit makes sense for sequences.
A set is a sequential preconvergence space if it comes with a binary relation between the set of all sequences in and itself, for and . A sequential preconvergence space is sequentially Hausdorff if the binary relation is a functional relation, and every sequentially Hausdorff sequential preconvergence space has a partial function
Last revised on December 5, 2022 at 04:52:29. See the history of this page for a list of all contributions to it.