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Book review

Author(s) Gähler, W. (ed.)
Herrlich, H. (ed.)
Preuss, G. (ed.)
Title Recent developments of general topology and its applications - International Conference in Memory of Felix Hausdorff (1868-1942)
Publisher Akad. Verlag
Year of publication 1992
Reviewed by JAN PASEKA

The time of publishing (1992) this proceedings is both the anniversary of one of the main founders of topology - Felix Hausdorff and the hundredth anniversary of the publication of Poincare's first note on topology. The beginning of general topology, also called "point set topology", dates fourteen years later when Frechet published the first abstract treatment of the subject in 1906. 1914 appears the first textbook on general topology "Grundzüge der Mengenlehre" masterly written by Hausdorff. This pioneering monograph secured his international reputation and it was a breakpoint from that the rapid development of classical topology begun. Modern general topology involves such research areas as dimension theory, extension and completion problems, nearness and convergence structures, distance spaces, fractal geometry, fuzzy topology, "pointless topology" and applies to functional analysis and to set theory and logic.

The purpose of this book is to make recent developments of general topology accessible to everyone who is or will be interested in the presented area. Let us list the 36 articles and their authors: A.V. Arhangel'skii, Divisibility and cleavability of spaces, A. Bella, A couple of questions concerning nowhere constant continuous functions, H.L. Bentley, Strict extensions of Tl spaces, H.L. Bentley and H. Herrlich, Compactness=Completness n Total boundedness - a natural example of a non-reflective intersection of reflective subcategories, R. Börger, How to make a path injective, G.C.L. Brümmer, Completions of Functorial Topological Structures, G. Castellini, J. Koslowski and G.E. Strecker, Categorical closure operators via Galois connections, S. Dolecki and R. Peirone, Topological semigroups of every countable sequential order, E. Eichhorn, Felix Hausdorff- Paul Mongré: Some Aspects of his Life and the Meaning of his Death, P. Eklund and W. Gähler, Contributions to fuzzy convergence, R. Fric, On completions of rationals, S. Gähler and W. Gähler, Generalized topologies generated by distance functions, W. Gähler, Monadic topology - A new concept of generalized topology, U. Höhle, On the equivalence between ß-algebras and compact Hausdorff spaces in the framework of Lukasiewicz logic, Sung Sa Hong, Simple extensions of frames, M. Husek, History and development of Hausdorff's work in extension in metric spaces, I. Juhász, The cardinality and weight-spectrum of compact spaces, H. Kleisli and H.-P. Künzi, Topologies on totally convex spaces, D. Leseberg, Superconvergence spaces and related topics, H. Lord, Factorization and disconnectedness, R. Lowen and N. Robeys, Products of metric spaces, E. Lowen-Colebunders, Hausdorff separation for Cauchy spaces, E. Michael, Selection Theorems With and Without Dimensional Restrictions, Jun-iti Nagata, A survey of dimension theory V, Ryosuke Nakagawa, Separation axioms for fuzzy topological spaces, L.D. Nel, Effective categories of complete separated spaces, M.C. Pedicchio, On Grothendieck quasi-topoi, H. Poppe, On Hausdorff convergence of graphs of functions, J. Porter, Hausdorff-closed extensions and Tychonoff, G. Preuss, Semiuniform limit spaces and semi-Cauchy spaces, H.-Ch. Reichel, Distance-functions as a unifying concept in the theory of generalized metric spaces, G. Richter, Algebraically behaved categories of ordered Hausdorff spaces, S. Salbany and S. Romaguera, The Hausdorff extension theorem for distance spaces, F. Schwarz, Hulls of classes of "gestufte Räume", V. Trnková, Rigid points and rigidity-creating properties, P. Vojtás, Topological cardinal invariants and the Galois-Tukey category.

These are well-known and most respected names and their articles constitute a quite valuable survey of the recent developments in this field. So, the book represents a sound investment for each good library.