Dieudonné-Schwartz theorem in inductive limits of metrizable spaces
Dieudonné-Schwartz theorem in inductive limits of metrizable spaces
The Dieudonné-Schwartz Theorem for bounded sets in strict inductive limits does not hold for general inductive limits <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E equals i n d limit upper E Subscript n"> <mml:semantics> <mml:mrow> <mml:mi>E</mml:mi> <mml:mo>=</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi>ind</mml:mi> </mml:mrow> <mml:mo movablelimits="true" form="prefix">lim</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>E</mml:mtext> </mml:mrow> …