On c-sets and products of ideals

Marek Balcerzak

Colloquium Mathematicae (1991)

  • Volume: 62, Issue: 1, page 1-6
  • ISSN: 0010-1354

Abstract

top
Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.

How to cite

top

Balcerzak, Marek. "On c-sets and products of ideals." Colloquium Mathematicae 62.1 (1991): 1-6. <http://eudml.org/doc/210094>.

@article{Balcerzak1991,
abstract = {Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.},
author = {Balcerzak, Marek},
journal = {Colloquium Mathematicae},
keywords = {products of ideals; Polish spaces; -finite Borel measure; - sets; -saturated},
language = {eng},
number = {1},
pages = {1-6},
title = {On c-sets and products of ideals},
url = {http://eudml.org/doc/210094},
volume = {62},
year = {1991},
}

TY - JOUR
AU - Balcerzak, Marek
TI - On c-sets and products of ideals
JO - Colloquium Mathematicae
PY - 1991
VL - 62
IS - 1
SP - 1
EP - 6
AB - Let X, Y be uncountable Polish spaces and let μ be a complete σ-finite Borel measure on X. Denote by K and L the families of all meager subsets of X and of all subsets of Y with μ measure zero, respectively. It is shown that the product of the ideals K and L restricted to C-sets of Selivanovskiĭ is σ-saturated, which extends Gavalec's results.
LA - eng
KW - products of ideals; Polish spaces; -finite Borel measure; - sets; -saturated
UR - http://eudml.org/doc/210094
ER -

References

top
  1. [1] M. Balcerzak, Remarks on products of σ-ideals, Colloq. Math. 56 (1988), 201-209. Zbl0679.28003
  2. [2] J. P. Burgess, Classical hierarchies from a modern stand-point, Part I, C-sets, Fund. Math. 115 (1983), 80-95. 
  3. [3] D. Cenzer and R. D. Mauldin, Inductive definability: measure and category, Adv. in Math. 38 (1980), 55-90. Zbl0466.03018
  4. [4] J. Cichoń and J. Pawlikowski, On ideals of subsets of the plane and on Cohen reals, J. Symbolic Logic 51 (1986), 560-569. Zbl0622.03035
  5. [5] M. Gavalec, Iterated products of ideals of Borel sets, Colloq. Math. 50 (1985), 39-52. Zbl0604.28001
  6. [6] A. S. Kechris, Measure and category in effective descriptive set theory, Ann. Math. Logic 5 (1972/73), 337-384. Zbl0277.02019
  7. [7] C. G. Mendez, On sigma-ideals of sets, Proc. Amer. Math. Soc. 60 (1976), 124-128. Zbl0348.28002
  8. [8] Y. N. Moschovakis, Descriptive Set Theory, North-Holland, Amsterdam 1980. 
  9. [9] E. A. Selivanovskiĭ, On a class of effective sets (C-sets), Mat. Sb. 35 (1928), 379-413 (in Russian). 
  10. [10] V. V. Srivatsa, Measure and category approximations for C-sets, Trans. Amer. Math. Soc. 278 (1983), 495-505. Zbl0525.04006
  11. [11] R. L. Vaught, Invariant sets in topology and logic, Fund. Math. 82 (1974), 269-294. Zbl0309.02068

NotesEmbed ?

top

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.