Geodesic
Topologies Determined by -Ideals on ω1
Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1306-1312

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Broverman, S.; Ginsburg, J.; Kunen, K.; Tall, F. D. Topologies Determined by -Ideals on ω1. Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1306-1312. doi: 10.4153/CJM-1978-107-7
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[1] 1. Baumgartner, J. E., A new class of order types, Ann. Math. Logic f (1976), 187–222. Google Scholar

[2] 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] 3. Comfort, W. W., A survey of cardinal invariants, Gen. Top. Appl. 1 (1971), 163–199. Google Scholar

[4] 4. Corson, H. H., Normality in subsets of product spares, Am. J. Math. 81 (1959), 785–790. Google Scholar

[5] 5. Devlin, K. J., Variations on (), preprint. Google Scholar

[6] 6. Devlin, K. J. and Johnsbraten, H., The Souslin Problem, Lect. Notes Math. (Springer-Verlag, Berlin). Google Scholar

[7] 7. Gillman, L. and Jerison, M., Rings of continuous functions (van Nostrand, Princeton, 1960). Google Scholar

[8] 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] 9. Jnhasz, I., Cardinal functions in topology, Mathematical Centre, Amsterdam, 1971. Google Scholar

[10] 10. Knnen, K., Combinatorics, in Handbook of mathematical logic North-Holland, Amsterdam, (1977), 371–401. Google Scholar

[11] 11. Ostaszewski, A. J., On countably compact, perfectly normal spaces, J. London Math. Soc. 2 U (1976), 505–516. Google Scholar

[12] 12. Shelah, S., Remarks on cardinal invariants in topology, Gen. Top. Appl. 7 (1977), 251–259. Google Scholar

[13] 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] 14. Tall, F. D., Some applications of a generalized Martin's Axiom, submitted for publication. Google Scholar

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