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Ferrera Cuesta, Juan
(1982)
*Spaces of weakly continuous functions.*
Pacific Journal of Mathematics, 102
(2).
pp. 285-291.
ISSN 0030-8730

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## Abstract

This paper is very much in the spirit of a paper by H. Corson [Trans. Amer. Math. Soc. 101 (1961),

1–15; MR0132375 (24 2220)]. Let E be a real Banach space. The bw-topology on E is the finest

topology which agrees with the weak topology on all bounded subsets of E. Cwb(E) [Cwbu(E)]

is the set of real functions which are weakly continuous [weakly uniformly continuous] on all

bounded sets in E. Cwb(E) is always barrelled; a sufficient condition is given for Cwb(E) to be

bornological (under the compact-open topology). As a main result, the following are shown to be

equivalent: (1) E is reflexive; (ii) Cwbu(E) is a Fr´echet space; (iii) Cwbu(E) is a Pt´ak space; (iv)

Cwbu(E) is complete; (v) Cwbu(E) is barrelled; (vi) Cwbu(E) = Cwb(E).

Item Type: | Article |
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Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 15380 |

Deposited On: | 28 May 2012 08:33 |

Last Modified: | 09 Aug 2018 09:19 |

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