Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introdu...Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for ( DST ). These results improve relevant earlier results.展开更多
文摘Let (E,ζ)= indlim (E n ,ζ n ) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (E n ,ζ n ). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for ( DST ). These results improve relevant earlier results.
