Skip to main content Accessibility help

Two step iteration of almost disjoint families

  • Jerry E. Vaughan (a1)


Let E be an infinite set, and [E]ω the set of all countably infinite subsets of E. A family ⊂ [E]ω is said to be almost disjoint (respectively, pairwise disjoint) provided for A, B, if AB then AB is finite (respectively, AB is empty). Moreover, an infinite family A is said to be a maximal almost disjoint family provided it is an infinite almost disjoint family not properly contained in any almost disjoint family. In this paper we are concerned with the following set of topological spaces defined from (maximal) almost disjoint families of infinite subsets of the natural numbers ω.



Hide All
[1]Gilman, L. and Jerison, M., Rings of continuous functions, D. Van Nostrand Co. Inc., Princeton, 1960.
[2]Hechler, Stephen H., Short complete nested sequences in βN\N and small maximal almost-disjoint families, General Topology and its Applications, vol. 2 (1972), pp. 139149.
[3]Mrówka, S., On completely regular spaces, Fundamenta Mathematicae, vol. 41 (1954), pp. 105106.
[4]Mrówka, S., Some set-theoretic constructions in topology, Fundamenta Mathematicae, vol. 94 (1977). no. 2, pp. 8392.
[5]Nyikos, P., Soukup, L., and Veličković, B., Hereditary normality of γN-spaces, Topology and its Applications, vol. 65 (1995), no. 1, pp. 919.
[6]Nyikos, Peter J. and Vaughan, Jerry E., The Scarborough-Stone problem for Hausdorff spaces, Topology and its Applications, vol. 44 (1992), no. 1–3, pp. 309316.
[7]Scarborough, C. T. and Stone, A. H., Products of nearly compact spaces, Transactions of the Amererican Mathematical Society, vol. 124 (1966), pp. 131147.
[8]Shelah, S., Are and your cup of tea?, (publication number 700).
[9]Urysohn, P., Über die Mächtigkeit der zusammenhängenden Mengen, Mathematische Annalen vol. 94 (1925), pp. 262295.
[10]van Douwen, E. K., The integers and topology, Handbook of set-theoretic topology (Kunen, K. and Vaughan, J. E., editors), North-Holland, Amsterdam, 1984, pp. 111167.
[11]Vaughan, J. E., Products of perfectly normal, sequentially compact spaces, Journal of London Mathematical Society (2), vol. 14 (1976), pp. 517520.
[12]Vaughan, J. E., Small uncountable cardinals and topology, Open problems in topology (van Mill, J. and Reed, G. M., editors), North-Holland Publishing Co., Amsterdam, 1990, pp. 195218.
[13]Vaughan, J. E., Almost disjoint families and iterations of Ψ. Abstracts of the American Mathematical Society, vol. 81 (1992), no. 874–54–102, p. 319.


Related content

Powered by UNSILO

Two step iteration of almost disjoint families

  • Jerry E. Vaughan (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.