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property D; pseudonormal; first countable; Cohen model
In answer to a question of M. Reed, E. van Douwen and M. Wage [vDW79] constructed an example of a Moore space which had property D but was not pseudonormal. Their construction used the Martin's Axiom type principle $P(c)$. We show that there is no such space in the usual Cohen model of the failure of CH.
[Dow92] Dow A.: Set Theory in Topology. in Recent progress in general topology (Prague, 1991); North-Holland, Amsterdam, 1992, pp.167-197. MR 1229125 | Zbl 0796.54001
[Kun83] Kunen K.: Set Theory. volume 102 of {Studies in Logic and the Foundations of Mathematics}; North-Holland Publishing Co., Amsterdam, 1983; An introduction to independence proofs, Reprint of the 1980 original. MR 0597342 | Zbl 0960.03033
[vDW79] van Douwen E.K., Wage M.L.: Small subsets of first countable spaces. Fund. Math. 103 2 103-110 (1979). MR 0543872 | Zbl 0425.54013
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