This book is an expanded proceedings of Prague Toposym 1991 which was held in Prague, Czechoslovakia, August 19--23, 1991. The Prague topology symposia are held every five years. The editors intended this particular symposium to be an attempt to update previous works [Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984; MR 85k:54001; Open problems in topology, North-Holland, Amsterdam, 1990; MR 92c:54001]. The Handbook is a fairly complete account of set-theoretic topology up to 1984. The Open problems volume presents about 1100 problems in topology which were open in 1990. The contributors that were solicited in Open problems were a remarkable collection of experts in their fields. The stature of the contributors to Open problems made the volume an especially complete compendium on the state of topology at the date. Open problems also attempted to be comprehensive in its coverage of topology.

It would perhaps be helpful to classify the reports under the eight headings given in Open problems. This listing follows below. Set-theoretic topology: "Set theory in topology" by Dow; "Descriptive topology" by Hansell; and "Cardinal functions" by Juhasz. General topology: "Sequential convergence spaces" by Fric and Koutnik; "Generalized metric spaces and metrization" by Gruenhage; "The Cech-Stone compactification of the real line" by Hart; "Special metrics" by Hattori and Nagata; "Extensions of mappings" by Hoshina; "Covering properties" by Junnila; "Convergence in topology" by Nyikos; "Compact spaces and their generalizations" by Shakhmatov; and "The construction of topological spaces" by Watson. Continua theory: "Continuum theory" by Mayer and Oversteegen. Topology and algebraic structures: "Topological groups and semigroups" by Comfort, Hofmann and Remus. Topology and computer science: None of the reports fall under this classification. Algebraic and geometric topology: "Topological classification of infinite-dimensional spaces with absorbers" by Dijkstra and van Mill. Topology arising from analysis: "$C\sb p$-theory" by Arkhangel skii; "Banach spaces and topology. II" by Mercourakis and Negrepontis. Dynamics: "Abstract topological dynamics" by de Vries.

The reports "Categorical topology" by Herrlich and Husek and "Topology and differentiation theory" by Frolicher and Kriegl do not fit into the classifications in Open problems.

The volume under review is related to the Handbook and Open problems, but should not be seen as a comprehensive treatment of recent progress in general topology. Mary Ellen Rudin points out in the introduction that important results by Brian Lawrence concerning box products were not reported and that other areas were neglected as well. One would have expected some report on the recent results in dimension theory flowing from the theorem of A. N. Dranishnikov that there exists a compact metric space $X$ of integral cohomological dimension three, $\roman c$-$\dim\sb ZX=3$, and with infinite covering dimension, $\dim X=\infty$ [A. N. Dranishnikov, Mat. Sb. (N.S.) 135(177) (1988), no. 4, 551--557, 560; MR 90e:55004]. A great deal of new insight into shape theory has also come out of Dranishnikov's result and perhaps should also have found its way into this volume. There are no advances reported in finite-dimensional geometric topology, none in knot theory and none in algebraic topology. The report by de Vries on topological dynamics emphasizes a certain topological perspective in dynamics. From a different topological perspective, many other advances could have been reported. In the area of continuum theory, the article by Mayer and Oversteegen includes some results concerning complex dynamics and Julia sets as well as general continuum theory. There is another aspect of continuum theory and dynamical systems due to R. F. Williams. This is the relationship of attractors to inverse limits by means of branched manifolds with single bonding maps. This area has also had progress and a report would have fit nicely into a more comprehensive symposium.

General topology is a very diverse field, requires an extensive variety of tools, and applies widely to other areas of mathematics. There is considerable diversity represented in the twenty reports that make up this volume. There is some degree of uneven treatment and some topics have been left out. There is no point in making a comprehensive catalogue of what has been left out. One needs to remember a statistic that Stanislaw Ulam liked to point out: there are 200,000 theorems published in mathematics each year. In a five year period this amounts to a million theorems in print. Any effort at organizing even a portion of these results into some coherent form is a vital and welcome scholarly activity. We have such an effort in this volume which helps produce a viewpoint for the field of general topology.