Title




Pointwise bornological vector spaces
 
Author




 
Abstract




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, SpringerVerlag, Berlin, Heidelberg, New York. 1976, J Schmets, Spaces of VectorValued Functions, Lecture Notes in Math. vol 1003. SpringerVerlag, 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 vectorvalued continuous functions, in Proceedings Vector Space Measures and Applications I, Dublin, 1977. in Lecture Notes in Math, vol 644, SpringerVerlag, Berlin. Heidelberg. New York. 1978, pp 368377, J Schmets, Bornological and ultrabornological C(X E) spaces, Manuscripta Math 21 (1977) 117133] 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 
 
Language




English
 
Source (journal)




Topology and its applications.  Amsterdam
 
Source (book)




Conference on Advances in SetTheoretic Topology held in honor of, Tsugunori Nogura on his 60th Birthday, June 0919, 20082009, Erice, ITALY
 
Publication




Amsterdam
:
Elsevier Science
,
2010
 
ISSN




01668641
 
Volume/pages




157
:8
(2010)
, p. 15581568
 
ISI




000277677500031
 
Full text (Publisher's DOI)




 
