Pointwise bornological vector spaces
Faculty of Sciences. Mathematics and Computer Science

article

2010
Amsterdam :Elsevier Science
, 2010

Mathematics

Topology and its applications. - Amsterdam

Conference on Advances in Set-Theoretic Topology held in honor of, Tsugunori Nogura on his 60th Birthday, June 09-19, 2008-2009, Erice, ITALY

157(2010)
:8
, p. 1558-1568

0166-8641

000277677500031

E

English (eng)

University of Antwerp

The existing duality between topological and homological vector spaces allows us to define homological objects in the category of topological vector spaces For a Tychonoff space X and a set B of relatively pseudocompact subsets of X. the vector space C(X) endowed with the topology of uniform convergence on elements of B is a locally convex topological vector space, the homological coreflection of which is described in [J Schmets, Espaces de Fonctions Continues, Lecture Notes in Math. vol 519, Springer-Verlag, Berlin, Heidelberg, New York. 1976, J Schmets, Spaces of Vector-Valued Functions, Lecture Notes in Math. vol 1003. Springer-Verlag, Berlin. Heidelberg. New York, 1983, J Dontchev, S Salbany, V Valov. Barrelled and homological function spaces. J Math Anal Appl 242 (2000) 117, J Schmets, Spaces of vector-valued continuous functions, in Proceedings Vector Space Measures and Applications I, Dublin, 1977. in Lecture Notes in Math, vol 644, Springer-Verlag, Berlin. Heidelberg. New York. 1978, pp 368-377, J Schmets, Bornological and ultrabornological C(X E) spaces, Manuscripta Math 21 (1977) 117-133] If the elements of B are not supposed to he relatively pseudocompact, then this topology is no longer a vector topology and the bounded sets do not form a homology. so the classical theory on bornologicity cannot be applied to it The aim of this paper is to extend the duality between topological and homological vector spaces to larger classes of objects and, moreover, apply it to C(X) endowed with three different, natural topologies (C) 2009 Elsevier B V All rights reserved

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