The structure of the fréchet space s regarding the series ∑ƒn(xn)
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Open Access
|Nov 2012Abstract
We investigate the subsets of the Fr´echet space s of all sequences of real numbers equipped with the Fr´echet metric ρ from the Baire category point of view. In particular, we concentrate on the “convergence” sets of the series ∑ƒ<sub>n</sub> (x<sub>n</sub>) that is, sets of sequences x = (x<sub>n</sub>) for which the series converges, or has a sum (perhaps infinite), or oscillates. Provided all ƒ<sub>n</sub> are continuous real functions, sufficient conditions are given for the “convergence” sets to be of the first Baire category or residual in s.
Language: English
Page range: 1 - 8
Published on: Nov 12, 2012
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 times per year
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© 2012 Tibor Šalát, Peter Vadovič, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.