Remarks on chain conditions in products

Stevo Todorčević

Compositio Mathematica (1985)

  • Volume: 55, Issue: 3, page 295-302
  • ISSN: 0010-437X

How to cite


Todorčević, Stevo. "Remarks on chain conditions in products." Compositio Mathematica 55.3 (1985): 295-302. <>.

author = {Todorčević, Stevo},
journal = {Compositio Mathematica},
keywords = {ccc; Souslin line; cellular family; Souslin numbers; Kurepa number; cellular number; non-finitely productive property; -chain condition; ZFC},
language = {eng},
number = {3},
pages = {295-302},
publisher = {Martinus Nijhoff Publishers},
title = {Remarks on chain conditions in products},
url = {},
volume = {55},
year = {1985},

AU - Todorčević, Stevo
TI - Remarks on chain conditions in products
JO - Compositio Mathematica
PY - 1985
PB - Martinus Nijhoff Publishers
VL - 55
IS - 3
SP - 295
EP - 302
LA - eng
KW - ccc; Souslin line; cellular family; Souslin numbers; Kurepa number; cellular number; non-finitely productive property; -chain condition; ZFC
UR -
ER -


  1. [1] U. Avraham and S. Shelah: Martin's Axiom does not imply every two N1-dense sets of reals are isomorphic. Israel J. Math.38 (1980) 161-176. Zbl0457.03048MR599485
  2. [2] U. Avraham, M. Rubin and S. Shelah: On the consistency of some partition theorems for continuous colorings, and the structure of N1-dense real order types. Zbl0585.03019
  3. [3] J.E. Baumgartner: All N1-dense sets of reals can be isomorphic. Fund. Math.79 (1973) 101-106. Zbl0274.02037MR317934
  4. [4] J.E. Baumgartner: Order types of real numbers and other uncountable orderings. I. Rival (ed.), Ordered sets (1981) 239-277 (D. Reidel Publ. Co.). Zbl0506.04003MR661296
  5. [5] R. Bonnet: Sur les algèbres de Boole rigides, Thesis. Lyon: Université Claude-Bernard (1978). 
  6. [6] W.W. Comfort and S. Negrepontis: Chain conditions in topology. (Cambridge: Cambridge University Press (1982)). Zbl0488.54002MR665100
  7. [7] W.G. Fleissner: Some spaces related to topological inequalities proved by the Erdös-Rado theorem. Proc. Amer. Math. Soc.71 (1978) 313-320. Zbl0411.54007MR493930
  8. [8] F. Galvin: Chain conditions and products. Fund. Math.108 (1980) 33-42. Zbl0366.04011MR585558
  9. [9] F. Galvin and S. Shelah: Some counterexamples in the partition calculus. J. Comb. TheoryA15 (1973) 157-174. Zbl0267.04006MR329900
  10. [10] K. Kuratowski: Topology I. Academic Press (1966). Zbl0158.40802MR217751
  11. [11] D. Kurepa: La condition de Soslin et une propriété caractéristique des nombres réels. Comp. Rendus (Paris) 231 (1950) 1113-1114. Zbl0040.16602MR38401
  12. [12] D. Kurepa: On an inequality concerning cartesian multiplication, Gen. Topology and its relations to Modern Analysis and Algebra. Proc. Symp. Prague (1961) 258-259. Zbl0111.18403MR175792
  13. [13] D. Kurepa: The cartesian multiplication and the cellularity number. Publ. Inst. Math.2(16) (1962) 121-139. Zbl0127.25003MR177894
  14. [14] E. Marczewski: Séparabilité et multiplication cartésienne des espaces topologiques. Fund. Math.34 (1947) 127-143. Zbl0032.19104MR21680
  15. [15] E. Michael: Paracompactness and the Lindelöf property in finite and countable cartesian products. Compositio Math.23 (1971) 199-214. Zbl0216.44304MR287502
  16. [16] W.J. Mitchell: Aronszajn trees and the independence of the transfer property. Ann. Math. Logic5 (1972) 21-46. Zbl0255.02069MR313057
  17. [17] J. Roitman: Adding a random or a Cohen real. Fund. Math.103 (1979) 47-60. Zbl0442.03034MR535835
  18. [18] W. Sierpiński: Sur un problème concernant les sous-ensembles croissants du continu. Fund. Math3 (1922) 109-112. Zbl48.0206.01JFM48.0206.01
  19. [19] W. Sierpiński: Sur un problème concernant les types de dimensions, Fund. Math.19 (1932) 65-71. Zbl0005.19702JFM58.0632.04
  20. [20] S. Todorčević: Chain conditions in products. Abstracts Amer. Math. Soc.4: 3 (1983) 291-232. 

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.