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April 2005 Projective limits of paratopological vector spaces
Carmen Alegre
Bull. Belg. Math. Soc. Simon Stevin 12(1): 83-93 (April 2005). DOI: 10.36045/bbms/1113318132


In this paper we describe various methods of constructing new paratopological vector spaces from given ones. First, we introduce the notion of a right dual of a paratopological vector space with the aim to define a right weak topology. We prove that, in a certain class of normed spaces, the classical weak topology is determined by a right weak topology. Next, the quotient topology in the context of paratopological vector spaces is discussed. Finally, we consider the projective limit of paratopological vector spaces and prove that every pseudoconvex space is a projective limit of quasi-normed spaces.


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Carmen Alegre. "Projective limits of paratopological vector spaces." Bull. Belg. Math. Soc. Simon Stevin 12 (1) 83 - 93, April 2005.


Published: April 2005
First available in Project Euclid: 12 April 2005

zbMATH: 1089.46003
MathSciNet: MR2134859
Digital Object Identifier: 10.36045/bbms/1113318132

Primary: 46A03 , 46A16 , 54E35 , 54H11

Keywords: continuous linear map , paratopological vector space , projective limit , pseudoconvex , quasi-norm , quotient topology , right weak topology

Rights: Copyright © 2005 The Belgian Mathematical Society


Vol.12 • No. 1 • April 2005
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