Sequentially complete
In mathematics, specifically in topology and functional analysis, a subspace S of a topological vector space (TVS) X is said to be sequentially complete or semi-complete if every Cauchy sequence in S converges to an element in S. We call X sequentially complete if it is a sequentially complete subset of itself.
Examples
Every complete space is sequentially complete but not conversely. If a TVS is metrizable then it is complete if and only if it is sequentially complete.
See also
- Cauchy net
- Complete space
- Topological vector space
- Uniform space
References
- Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. 3. New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.CS1 maint: ref=harv (link)
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