On the property (db) for continuous function spaces

Render, Hermann

doi:10.1016/s0166-8641(97)00235-6

Cited by 1 publication

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“…Distinguishing examples appear in [34] and in [25], and, in the latter work, Saxon and Narayanaswami give applications to the separable quotient problem for Fréchet spaces and to open mapping theorems. Specifically, we aim to characterize those C κ (X) that are (db)-spaces in terms of topological properties of X, thereby answering a question of Todd [30] and supporting both the joint announcement of the present authors [31] and the Corrigendum to [18] of Render [19]. In so doing, we also give characterizations of property (db) and examples of spaces X that distinguish between the (db)-property and the weaker and stronger properties of C κ (X), Bairelike and unordered Bairelike.…”

Section: Introductionmentioning

confidence: 64%

Continuous function spaces, (db)-spaces and strongly Hewitt spaces

Todd

Render²

2004

Topology and its Applications

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We solve the long standing problem of characterizing those Tychonov spaces X for which the function space, C κ (X), of realvalued continuous functions with the compact-open topology satisfies property (db). This property is one of a spectrum of algebraic-topological properties previously known to be distinct for locally convex spaces: In increasing strength, these properties are barrelled, Bairelike, property (db), unordered Bairelike, and Baire. Strongly Hewitt spaces, recently defined and studied by Kakol andŚliwa, are characterized here using unbounded filters on X, which shows that C κ (X) is a (db)-space. We give examples of C κ (X) distinguishing property (db) within the above spectrum and from those C κ (X) with X strongly Hewitt, answer a question of Kakol, and state some further problems.  2004 Elsevier B.V. All rights reserved. MSC: primary 54C35; secondary 54E52

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