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Article

Malykhin, V. I.
$C_p(I)$ is not subsequential. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 40 (1999), issue 4, pp. 785-788
MSC: 03E35, 54A20, 54A25, 54A35 | MR 1756553 | Zbl 1009.54033
Keywords:
$C_p$-space; sequential; subsequential
Summary:
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its $C_p$-space is not subsequential.
References:
[1] Arhangel'skii A.V.: Topological Function Spaces. Kluwer Dordrecht, Boston, London 54 (1992).
[2] Malykhin V.I.: On subspaces of sequential spaces. Math. Notes (in Russian) 64 (1998), 3 407-413. MR 1680130
[3] Pytke'ev E.G.: On maximally resolvable spaces. Proc. Steklov Institute of Mathematics (1984), 154 225-230.
[4] Malykhin V.I., Tironi G.: Weakly Fréchet-Urysohn spaces. Quaderni Matematica, II Serie, Univ. di Trieste (1996), 386 1-9.
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