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separable; c.c.c.; $\sigma$-centered base; $\sigma$-$n$-linked base; $I_n$-em\-bed\-ding; $I_{<\omega}$-em\-bed\-ding; product; Martin's Axiom; $C_p$-spaces
We characterize spaces with $\sigma$-$n$-linked bases as specially embedded subspaces of separable spaces, and derive some corollaries, such as the $\bold c$-productivity of the property of having a $\sigma$-linked base.
[A] Arhangel'skii A.V.: Topological function spaces. Mathematics and its applications (Soviet Series) 78, Kluwer Academic Publishers Group, Dordrecht, 1992. MR 1144519
[BvD] Baumgartner J.E., van Douwen E.K.: Strong realcompactness and weakly measurable cardinals Topology Appl. 35 (1990), 239-251. MR 1058804
[BM] Bonanzinga M., Matveev M.V.: Products of star-Lindelöf and related spaces. in preparation. Zbl 0983.54006
[B1] Borges C.R.: Extension properties of $K_i$-spaces Questions Answers Gen. Topology. 7 (1989), 81-97. MR 1026403
[B2] Borges C.R.: Extensions of real-valued functions Questions Answers Gen. Topology. 14 (1996), 233-243. MR 1403348
[vDTh] van Douwen E.K.: Simultaneous extension of continuous functions. Thesis, Vrije Univ., Amsterdam (1975): E. K. van Douwen, {Collected Papers}, Ed. by J. van Mill, North Holland, 1994, pp.67-171.
[vD0] van Douwen E.K.: Simultaneous linear extension of continuous functions Topology Appl. 5 (1975), 297-319. MR 0380715
[vD1] van Douwen E.K.: Density of compactifications. Set-theoretic Topology, G.M. Reed ed., N.Y., 1977, pp.97-110. MR 0442887 | Zbl 0379.54006
[vD2] van Douwen E.K.: The Pixley-Roy topology on spaces of subsets. Set-theoretic Topology, G.M. Reed ed., N.Y., 1977, pp.111-134. MR 0440489 | Zbl 0372.54006
[K] Kuratowski K.: Topology I. Academic Press, New York, 1966. MR 0217751 | Zbl 0849.01044
[LMcD] Levy R., McDowell R.H.: Dense subsets of $\beta X$. Proc. Amer. Math. Soc. 507 (1975), 426-429. MR 0370506 | Zbl 0313.54025
[SW] Steprans J., Watson S.: Cellularity of first countable spaces. Topology Appl. 28 (1988), 141-145. MR 0932978 | Zbl 0634.54015
[T] Tall F.: Normality versus collectionwise normality. Handbook of Set-theoretic Topology, K. Kunen and J. E. Vaughan eds., Elsevier Sci. Pub. B.V., 1984, pp.685-732. MR 0776634 | Zbl 0552.54011
[W] Weiss W.: Versions of Martin's axiom. Handbook of Set-theoretic Topology, K. Kunen and J. E. Vaughan, eds., Elsevier Sci. Pub. B.V., 1984, pp.827-886. MR 0776619 | Zbl 0571.54005
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