This Handbook is an introduction to set-theoretic topology for students in the field and for researchers in other areas for whom results in set-theoretic topology may be relevant. The aim of the editors has been to make it as self-contained as possible without repeating material which can easily be found in standard texts. The Handbook contains detailed proofs of core results, and references to the literature for peripheral results where space was insufficient. Included are many open problems of current interest.
In general, the articles may be read in any order. In a few cases they occur in pairs, with the first one giving an elementary treatment of a subject and the second one more advanced results. These pairs are: Hodel and Juhász on cardinal functions; Roitman and Abraham-Todorčević on S- and L-spaces; Weiss and Baumgartner on versions of Martin's axiom; and Vaughan and Stephenson on compactness properties.
1. Cardinal Functions I (R. Hodel). 2. Cardinal Functions II (I. Juhász). 3. The Integers and Topology (E.K. van Douwen). 4. Box Products (S.W. Williams). 5. Special Subsets of the Real Line (A.W. Miller). 6. Trees and Linearly Ordered Sets (S. Todorčević). 7. Basic S and L (J. Roitman). 8. Martin's Axiom and First Countable S- and L-Spaces (U. Abraham and S. Todorčević). 9. Covering Properties (D.K. Burke). 10. Generalized Metric Spaces (G. Gruenhage). 11. An Introduction to &bgr;&ugr; (J. van Mill). 12. Countably Compact and Sequentially Compact Spaces (J.E. Vaughan). 13. Initially k-Compact and Related Spaces (R.M. Stephenson Jr.). 14. The Theory of Nonmetrizable Manifolds (P. Nyikos). 15. Normality versus Collectionwise Normality (F.D. Tall). 16. The Normal Moore Space Conjecture and Large Cardinals (W.G. Fleissner). 17. Dowker Spaces (M.E. Rudin). 18. Products of Normal Spaces (T.C. Przymusiński). 19. Versions of Martin's Axiom (W. Weiss). 20. Random and Cohen Reals (K. Kunen). 21. Applications of the Proper Forcing Axiom (J.E. Baumgartner). 22. Borel Measures (R.J. Gardner and W.F. Pfeffer). 23. Banach Spaces and Topology (S. Negrepontis). 24. Topological Groups (W.W. Comfort).
- © North Holland 1984
- 1st November 1984
- North Holland
- eBook ISBN:
@qu:...an indispensable reference for many years to come ...a massive undertaking... I would recommend that anyone interested in general topology take a look at this book ...many set-theorists are going to want a copy of their own. @source:Stewart Baldwin The Journal of Symbolic Logic