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Some remarks on almost radiality in function spaces. (English) Zbl 0673.46013
Let \(C_ p(X)\) be the space of continuous real functions on X, a Hausdorff topological space, with the topology of pointwise convergence. It is known that this space is Fréchet if and only if it is “radial”, a notion defined with generalized sequences using ordinal numbers. It is also known that this space is not necessarily a Fréchet space if \(C_ p(X)\) is only “pseudo-radial”. The paper introduces and studies new kinds of “almost radiality” which coincides with “pseudo-radiality” in some specific cases.
Reviewer: H.Hogbe-Nlend

MSC:
46E10 Topological linear spaces of continuous, differentiable or analytic functions
46A04 Locally convex Fréchet spaces and (DF)-spaces
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