In functional analysis, a topological vector space (TVS) is said to be quasi-complete or boundedly complete[1] if every closed and bounded subset is complete.[2] This concept is of considerable importance for non-metrizable TVSs.[2]
Every complete TVS is quasi-complete.[7] The product of any collection of quasi-complete spaces is again quasi-complete.[2] The projective limit of any collection of quasi-complete spaces is again quasi-complete.[8] Every semi-reflexive space is quasi-complete.[9]
The quotient of a quasi-complete space by a closed vector subspace may fail to be quasi-complete.