International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 3, Pages 615-617
doi:10.1155/S016117128400065X
Bounded sets in fast complete inductive limits
Jan Kučera
and Carlos Bosch
Department of Mathematics, Washington State University, Pullman 99164, Washington, USA
Abstract
Let E1⊂E2⊂… be a sequence of locally convex spaces with all identity maps: En→En+1 continuous and E=indlim En fast complete. Then each set bounded in E is also bounded in some En iff for any Banach disk B bounded in E and n∈N, the closure of B⋂En in B is bounded in some Em. This holds, in particular, if all spaces En are webbed.