JP Journal of Geometry and Topology
Volume 7, Issue 3, Pages 423 - 456
(November 2007)
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DUALITY OF 
VECTOR SPACES, THEIR TOPOLOGIES AND APPLICATIONS
S. V. Ludkovsky (Russia)
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or C
or a field with a non-trivial non-archimedean valuation. For such spaces the
analog of the Mackey-Arens theorem is proved. A conditional
k-normability
of spaces
of linear topological
homeomorphisms of a locally convex k-normed
space X is studied, when an image of
elements under the corresponding operations is in
Cases, when
k-normability of a topological vector space implies its
local convexity, are investigated. Applications of k-normed spaces for resolutions of differential
equations and for approximations of functions in mathematical economy are
illustrated.
spaces, 
