Alan Dow

Ph.D. ... University of Manitoba ... February 1980
Dissertation: Contributions to the theory of absolute C-embeddings.
Supervisor: R.G. Woods


Research Interests

Methods from set theory, model theory, and especially the technique of forcing are applied to the study of general topological spaces. My interests are in the structure of topological spaces that are not ``too large'' or pathological but they will not be metrizable spaces. The types of spaces under investigation do regularly arise in areas such as functional analysis. A particularly important space is the Stone-Cech compactification of the integers. Many of the properties of these spaces are quite sensitive to the axioms of set theory and this is where the techniques from set theory are so important. A sample question (which remains unsolved) is to ask if an infinite compact space necessarily contains one of ``a converging sequence'' or ``a copy of the Stone-Cech compactification of the integers''. A sample question that is solved, if every subset of a compact space that has cardinality equal to the first uncountable cardinal is metrizable, then the entire space is metrizable. I am also interested in the study of Boolean algebras as they apply to topological spaces via Stone duality.

Selected PUBLICATIONS



Chapters in Books:

  1. bN.  Proceedings of the New York Academy of Sciences, Commemorative Issue to Mary Ellen Rudin, Ed. R. Kopperman and F.D. Tall, 47-66, 1993  . (A. Dow )

  2. Set theory in topology.  In Recent Progress in General Topology, M. Husek and J. van Mill (editors). Ch. 4, 168-197, Elsevier Science Publishers B.V., Amsterdam 1992. ( A. Dow )

  3. A compact non-sequential space A tribute to Paul Erdos, Ed. Baker, Bollobás, and Hajnal. 153-159, Cambridge University Press, 1990.

  4. Compact spaces of countable tightness in the Cohen model  Set Theory and its Applications, Springer Lecture Notes 1401, Eds. J. Steprans and S. Watson, (1989) 55-67.


Papers in Refereed Journals

  1. A universal continuum of weight À. Trans. Amer. Math. Soc., to appear (with Hart, Klaas Pieter)

  2. w* has (almost) no continuous images. Israel J. Math. 109 (1999), 29-39. (with Hart, Klaas Pieter)

  3. The regular open algebra of bR - R is not equal to the completion of P(w)/fin. Fund. Math. 157 (1998), no. 1, 33-41.

  4. Hereditary indecomposability and the Intermediate Value Theorem, Houston Journal, to appear (with Hart, Klaas Pieter)

  5. The measure algebra does not always embed, Fund. Math., to appear (with Hart, Klaas Pieter)

  6. Pseudoradial spaces: separable subsets, products and maps onto Tychonoff cubes, Topology and its Applications, to appear, (with A. Bella and G. Tironi)

  7. Two Real Ultrafilters on w, Top. Appl., (to appear), to appear (with J. Zhou)

  8. What I learned about bX, C(X) and products from Wis Comfort, Top. and Appl., (to appear).

  9. Extending real-valued functions in bk, Fund. Math. 152 (1997), no. 1, 21-41.

  10. On compact separable radial spaces, Canad. Math. Bull. 40 (1997), no. 4, 422-432.

  11. Weak covering properties of weak topologies. Proc. London Math. Soc., (3) 75 (1997), no. 2, 349-368. (with H. Junilla, J. Pelant)

  12. Depth, p-character, and tightness in superatomic Boolean algebras. Topology Appl. 75 (1997), no. 2, 183-199. (with D. Monk)

  13. Homogeneity in powers of zero-dimensional first-countable spaces. Proc. Amer. Math. Soc. 125 (1997), no. 8, 2503-2510. (with E. Pearl)

  14. On MAD families and sequential order.  Papers on general topology and applications (Amsterdam, 1994), 79-94, Ann. New York Acad. Sci., 788, 1996. ( A. Dow )

  15. Reaping numbers of Boolean algebras.  Bulletin of the London Mathematical Society, 28 (1996), 591-599. ( A. Dow, J. Steprans, S. Watson )

  16. On Boolean subalgebras of P(w1)/ctble, Journal of Symbolic Logic, J. Symbolic Logic 61 (1996), no. 3, 873-879.

  17. More set-theory for topologists, Topology and its applications 64 (1995) 243-300.

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On 01 Nov 2000, 09:39.