No hedgehog in the product?
Simon, Petr ; Tironi, Gino
Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002), p. 349-361 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 2002-01-01
Classification:  03E50,  03E65,  54B10,  54D55,  54G20
@article{119325,
     author = {Petr Simon and Gino Tironi},
     title = {No hedgehog in the product?},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {43},
     year = {2002},
     pages = {349-361},
     zbl = {1090.54024},
     mrnumber = {1922133},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119325}
}
Simon, Petr; Tironi, Gino. No hedgehog in the product?. Commentationes Mathematicae Universitatis Carolinae, Tome 43 (2002) pp. 349-361. http://gdmltest.u-ga.fr/item/119325/

Archangel'Skii A.V. The frequency spectrum of a topological space and the classification of spaces, Soviet. Math. Dokl. 13 (1972), 265-268. (1972)

Brendle J.; Laberge T. Forcing tightness of products of fans, Fund. Math. 150 3 (1996), 211-226. (1996)

Erdös P.; Shelah S. Separability properties of almost-disjoint families of sets, Israel J. Math. 12 (1972), 207-214. (1972)

Laberge T.; Landver A. Tightness in products of fans and pseudo-fans, Topology Appl. 65 (1995), 237-255. (1995)

Martin D.A.; Solovay R.M. Internal Cohen extension, Ann. Math. Logic 2 (1970), 143-178. (1970)

Michael E. A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. (1972)

Products of $\langle \alpha_i\rangle$-spaces, Nogura T. Topology Appl. 21 (1985), 251-259. (1985)

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.

Simon P. A hedgehog in the product, Acta. Univ. Carolin. Math. Phys. 39 (1998), 147-153. (1998)

Siwiec F. Sequence covering and countably bi-quotient mappings, Gen. Topology Appl. 1 (1971), 143-154. (1971)

Todorcevic S. Partition problems in topology, Contemporary Mathematics, 84, Amer. Math. Soc., Providence, RI, 1989.