Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
Fréchet space; $\alpha _4$-space; Fréchet fan; $(\kappa, \kappa )$-good set
Fréchet space; $\alpha _4$-space; Fréchet fan; $(\kappa, \kappa )$-good set
Summary:
Assuming OCA, we shall prove that for some pairs of Fréchet $\alpha_4$-spaces $X, Y$, the Fréchetness of the product $X\times Y$ implies that $X\times Y$ is $\alpha_4$. Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.
References:
[Ar] Archangel'skii A.V.: The frequency spectrum of a topological space and the classification of spaces. Soviet. Math. Dokl. 13 (1972), 265-268.
[BL] Brendle J., LaBerge T.: Forcing tightness of products of fans. Fund. Math. 150 3 (1996), 211-226.
[ES] Erdös P., Shelah S.: Separability properties of almost-disjoint families of sets. Israel J. Math. 12 (1972), 207-214.
[LL] LaBerge T., Landver A.: Tightness in products of fans and pseudo-fans. Topology Appl. 65 (1995), 237-255.
[MS] Martin D.A., Solovay R.M.: Internal Cohen extension. Ann. Math. Logic 2 (1970), 143-178.
[Mi] Michael E.: A quintuple quotient quest. Gen. Topology Appl. 2 (1972), 91-138.
[No] Products of $\langle \alpha_i\rangle$-spaces.
[Ny] Nyikos P.J.: Convergence in topology. in: Recent Progress in General Topology, ed. by M. Hušek and J. van Mill, North-Holland, 1992 pp.537-570.
[Si] Simon P.: A hedgehog in the product. Acta. Univ. Carolin. Math. Phys. 39 (1998), 147-153.
[Sw] Siwiec F.: Sequence covering and countably bi-quotient mappings. Gen. Topology Appl. 1 (1971), 143-154.
[To] Todorcevic S.: Partition problems in topology. Contemporary Mathematics, 84, Amer. Math. Soc., Providence, RI, 1989.
Search
Partner of
