No hedgehog in the product?

Petr Simon; Gino Tironi

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 2, page 349-361
  • ISSN: 0010-2628

Abstract

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Assuming OCA, we shall prove that for some pairs of Fréchet α 4 -spaces X , Y , the Fréchetness of the product X × Y implies that X × Y is α 4 . Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.

How to cite

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Simon, Petr, and Tironi, Gino. "No hedgehog in the product?." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 349-361. <http://eudml.org/doc/249006>.

@article{Simon2002,
abstract = {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.},
author = {Simon, Petr, Tironi, Gino},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fréchet space; $\alpha _4$-space; Fréchet fan; $(\kappa , \kappa )$-good set; Fréchet space; -space; Fréchet fan; ; )},
language = {eng},
number = {2},
pages = {349-361},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {No hedgehog in the product?},
url = {http://eudml.org/doc/249006},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Simon, Petr
AU - Tironi, Gino
TI - No hedgehog in the product?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 349
EP - 361
AB - 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.
LA - eng
KW - Fréchet space; $\alpha _4$-space; Fréchet fan; $(\kappa , \kappa )$-good set; Fréchet space; -space; Fréchet fan; ; )
UR - http://eudml.org/doc/249006
ER -

References

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  1. Archangel'skii A.V., The frequency spectrum of a topological space and the classification of spaces, Soviet. Math. Dokl. 13 (1972), 265-268. (1972) 
  2. Brendle J., LaBerge T., Forcing tightness of products of fans, Fund. Math. 150 3 (1996), 211-226. (1996) 
  3. Erdös P., Shelah S., Separability properties of almost-disjoint families of sets, Israel J. Math. 12 (1972), 207-214. (1972) 
  4. LaBerge T., Landver A., Tightness in products of fans and pseudo-fans, Topology Appl. 65 (1995), 237-255. (1995) 
  5. Martin D.A., Solovay R.M., Internal Cohen extension, Ann. Math. Logic 2 (1970), 143-178. (1970) 
  6. Michael E., A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. (1972) 
  7. Products of 〈 α i 〉 -spaces, Nogura T. Topology Appl. 21 (1985), 251-259. (1985) 
  8. 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. 
  9. Simon P., A hedgehog in the product, Acta. Univ. Carolin. Math. Phys. 39 (1998), 147-153. (1998) 
  10. Siwiec F., Sequence covering and countably bi-quotient mappings, Gen. Topology Appl. 1 (1971), 143-154. (1971) 
  11. Todorcevic S., Partition problems in topology, Contemporary Mathematics, 84, Amer. Math. Soc., Providence, RI, 1989. 

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