TY - JOUR
T1 - A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology
AU - Kraaij, Richard C.
PY - 2016/8/15
Y1 - 2016/8/15
N2 - Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β: the finest locally convex topology on the dual space that coincides with the weak topology on all weakly compact sets is a k-space. As a consequence, the space of bounded continuous functions with the strict topology is hypercomplete and a Pták space. Additionally, the closed graph, inverse mapping and open mapping theorems holds for linear maps between space of this type.
AB - Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β: the finest locally convex topology on the dual space that coincides with the weak topology on all weakly compact sets is a k-space. As a consequence, the space of bounded continuous functions with the strict topology is hypercomplete and a Pták space. Additionally, the closed graph, inverse mapping and open mapping theorems holds for linear maps between space of this type.
KW - Banach-Dieudonné theorem
KW - Closed graph theorem
KW - Space of bounded continuous functions
KW - Strict topology
UR - http://www.scopus.com/inward/record.url?scp=84975252117&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:47e2885d-581f-4185-9b51-b1e3dc7dab4e
U2 - 10.1016/j.topol.2016.06.003
DO - 10.1016/j.topol.2016.06.003
M3 - Article
AN - SCOPUS:84975252117
SN - 0166-8641
VL - 209
SP - 181
EP - 188
JO - Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology
JF - Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology
ER -