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Absorbing systems in infinite-dimensional manifolds. (English) Zbl 0794.57005
Summary: The aim of this paper is to define absorbing systems in infinite- dimensional manifolds and to derive some basic properties of them along the lines of T. A. Chapman [Trans. Am. Math. Soc. 154, 399-426 (1971; Zbl 0208.519)]. As an application we prove that for a countable nondiscrete Tykhonov space \(X\), if \(C_ p(X)\) is an \(F_{\sigma\delta}\) subset of \(\mathbb{R}^ X\) then it is an \(F_{\sigma\delta}\)-absorber, and hence homeomorphic to the countable infinite product of copies of \(\ell_ f^ 2\). This generalizes a result of T. Dobrowolski, W. Marciszewski and J. Mogilski [ibid. 328, No. 1, 307-324 (1991; Zbl 0768.54016)].

MSC:
57N20 Topology of infinite-dimensional manifolds
54C35 Function spaces in general topology
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