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Topologies Determined by -Ideals on ω1

Published online by Cambridge University Press:  20 November 2018

S. Broverman ,
J. Ginsburg ,
K. Kunen  and
F. D. Tall
S. Broverman
Affiliation:
University of Texas, Austin, Texas
J. Ginsburg
Affiliation:
University of Manitoba, Winnipeg, Manitoba
K. Kunen
Affiliation:
University of Wisconsin, Madison, Wisconsin
F. D. Tall
Affiliation:
University of Toronto, Toronto, Ontario
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σ-ideals (collections of sets which are closed under subset and countable union) are certainly important mathematically—consider first category sets, sets of measure zero, nonstationary sets, etc.—but aside from the observation that in certain spaces the first category σ-ideal is proper, cr-ideals have not been extensively studied by topologists. In this note we study a natural topology determined by a d-ideal, exploiting the interplay between the set-theoretic properties of the σ-ideal and the topological properties of the associated space.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1306 - 1312
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Baumgartner, J. E., A new class of order types, Ann. Math. Logic f (1976), 187–222.Google Scholar
2. Baumgartner, J. E., Almost-disjoint sets, the dense set problem and the partition calculus, Ann. Math. Logic 10 (1976), 401–439.Google Scholar
3. Comfort, W. W., A survey of cardinal invariants, Gen. Top. Appl. 1 (1971), 163–199.Google Scholar
4. Corson, H. H., Normality in subsets of product spares, Am. J. Math. 81 (1959), 785–790.Google Scholar
5. Devlin, K. J., Variations on (), preprint.Google Scholar
6. Devlin, K. J. and Johnsbraten, H., The Souslin Problem, Lect. Notes Math. (Springer-Verlag, Berlin).Google Scholar
7. Gillman, L. and Jerison, M., Rings of continuous functions (van Nostrand, Princeton, 1960).Google Scholar
8. Hajnal, A. and Jnhasz, I., .1 consequence of Martin s Axiom, Res. Paper 110, Dept. of Math., Univ. of Calgary, Calgary, Alberta.Google Scholar
9. Jnhasz, I., Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971.Google Scholar
10. Knnen, K., Combinatorics, in Handbook of mathematical logic North-Holland, Amsterdam, (1977), 371–401.Google Scholar
11. Ostaszewski, A. J., On countably compact, perfectly normal spaces, J. London Math. Soc. 2 U (1976), 505–516.Google Scholar
12. Shelah, S., Remarks on cardinal invariants in topology, Gen. Top. Appl. 7 (1977), 251–259.Google Scholar
13. Tall, F. D., The countable chain condition versus separability—applications of Martin's Axiom, Gen. Top. Appl. 4 (1974), 315–339.Google Scholar
14. Tall, F. D., Some applications of a generalized Martin's Axiom, submitted for publication.Google Scholar