Open AccessStrict topologies on spaces of vector-valued functions
Author(s) -
David Robbins
Publication year - 2010
Publication title -
acta et commentationes universitatis tartuensis de mathematica./acta et commentationes universitatis tartuensis de mathematica
Language(s) - English
Resource type - Journals
eISSN - 2228-4699
pISSN - 1406-2283
DOI - 10.12697/acutm.2010.14.08
Subject(s) - hausdorff space , locally convex topological vector space , disjoint sets , mathematics , topological vector space , vector space , completeness (order theory) , dual space , topological space , topology (electrical circuits) , regular polygon , space (punctuation) , disjoint union (topology) , pure mathematics , dual pair , normal space , combinatorics , topological tensor product , mathematical analysis , computer science , functional analysis , geometry , biochemistry , chemistry , gene , operating system
Let X be a completely regular Hausdorff space, and {Ex : x ∈ X} a collection of non-trivial locally convex topological vector spaces indexed by X. Let E be their disjoint union. We investigate a species of strict topology on a vector space F of choice functions σ : X → E (σ(x) ∈ Ex), and obtain Stone–Weierstrass and spectral synthesis analogues. We also obtain completeness results in some special cases.