4:["$","div",null,{"className":"min-h-screen bg-white flex flex-col","children":[["$","div",null,{"className":"px-6 pt-6 pb-4 border-b border-gray-100","children":[["$","div",null,{"className":"flex items-center gap-1.5 text-xs text-gray-400 mb-4","children":[["$","a",null,{"href":"/","className":"hover:text-[#26a69a] transition-colors","children":"Market"}],["$","span",null,{"children":"›"}],["$","span",null,{"className":"text-gray-600","children":"Sequentially complete"}]]}],["$","div",null,{"className":"text-[10px] text-gray-400 uppercase tracking-widest mb-1","children":"Company Profile"}],["$","h1",null,{"className":"text-2xl font-bold text-gray-900","children":"Sequentially complete"}],null]}],["$","div",null,{"className":"flex-1 px-6 py-6","children":[["$","p",null,{"className":"text-sm text-gray-600 leading-relaxed mb-8","children":"In mathematics, specifically in topology and functional analysis, a subspace S of a uniform space X is said to be sequentially complete or semi-complete if every Cauchy sequence in S converges to an element in S. \nX is called sequentially complete if it is a sequentially complete subset of itself."}],["$","div",null,{"className":"columns-1 md:columns-2 gap-10","children":[["$","div","0",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Sequentially complete topological vector spaces"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"Every topological vector space is a uniform space so the notion of sequential completeness can be applied to them. Properties of sequentially complete topological vector spaces • A bounded sequentially complete disk in a Hausdorff topological vector space is a Banach disk. • A Hausdorff locally convex space that is sequentially complete and bornological is ultrabornological. == Examples and sufficient conditions =="}}]]}],["$","div","1",{"className":"mb-8 break-inside-avoid","children":[["$","div",null,{"className":"text-xs font-semibold text-gray-400 uppercase tracking-wide mb-3 border-b border-gray-100 pb-1","children":"Examples and sufficient conditions"}],["$","div",null,{"className":"text-sm text-gray-600 leading-relaxed wiki-content","dangerouslySetInnerHTML":{"__html":"• Every complete space is sequentially complete but not conversely. • For metrizable spaces, sequential completeness implies completeness. Together with the previous property, this means sequential completeness and completeness are equivalent over metrizable spaces. • Every complete topological vector space is quasi-complete and every quasi-complete topological vector space is sequentially complete. == See also =="}}]]}]]}],["$","div",null,{"className":"mt-8 pt-4 border-t border-gray-100","children":["$","a",null,{"href":"https://en.wikipedia.org/wiki/Sequentially%20complete","target":"_blank","rel":"noopener noreferrer","className":"text-xs text-gray-400 hover:text-gray-600 transition-colors","children":"Source: Wikipedia ↗"}]}]]}],["$","div",null,{"className":"px-6 py-4 border-t border-gray-100 flex justify-between items-center","children":["$Lf","$L10"]}]]}]