Then it is a topological vector space
iff the scalar multiplication f (a) = ap is continuous on R for every fixed p [member of] V.
By a topological algebra we mean a topological vector space
A over K, which is also an associative algebra over K such that the multiplication in A is separately continuous (1).
Wilansky presents this mathematics text for advanced undergraduates and beginning graduate students on the subject of topological vector spaces
Treves, Topological Vector Spaces
, Distributions and Kernels, Academic Press, New York, 1967.
In Topological Vector Spaces
, Algebras and Related Areas.
of Maryland) presents an elementary introduction to topological vector spaces
and their most important application, the theory of distributions of Laurent Schwartz.
Their topics include contraction mappings, fixed point theorems in partially ordered sets, topological fixed point theorems, variational and quasivariational inequalities in topological vectors spaces and generalized games, best approximations and fixed point theorems for set-valued mappings in topological vector spaces
, degree theories for set-valued mappings, and nonexpansive types of mappings and fixed-point theorems in locally convex topological vector spaces
Invariant and quasiinvariant measures in infinite-dimensional topological vector spaces