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This book deals with algebraic topology, homotopy theory andsimple homotopy theory of infinite CW-complexes with ends. Contrary to most other works on these subjects, the current volumedoes not use inverse systems to treat these topics. Here, the homotopytheory is approached without the rather sophisticated notion ofpro-category. Spaces with ends are studied only by using appropriateconstructions such as spherical objects of CW-complexes in thecategory of spaces with ends, and all arguments refer directly to thiscategory. In this way, infinite homotopy theory is presented as anatural extension of classical homotopy theory. In particular, thisbook introduces the construction of the proper groupoid of a spacewith ends and then the cohomology with local coefficients is definedby the enveloping ringoid of the proper fundamental groupoid. This volume will be of interest to researchers whose work involvesalgebraic topology, category theory, homological algebra, generaltopology, manifolds, and cell complexes. ... Read more

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This book develops thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an 'almost ring'. Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions. The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras. ... Read more

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The book consists of articles at the frontier of current research in Algebraic Topology. It presents recent results by top notch experts, and is intended primarily for researchers and graduate students working in the field of algebraic topology. Included is an important article by Cohen, Johnes and Yan on the the homology of the space of smooth loops on a manifold M, endowed with the Chas-Sullivan intersection product, as well as an article by Goerss, Henn and Mahowald on stable homotopy groups of spheres, which uses the cutting edge technology of ... Read more

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The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext¹ (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators.
The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program.

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This workshop on Communication-Based Systems is intended topresent the research results of students of the Graduiertenkolleg`Communication-Based Systems' to an international community. Tostimulate the scientific discussion, renowned experts were invited togive their views on the following research areas:

• Formal specification and mathematical foundations of distributedsystems using process algebra, graph transformations, process calculi,and temporal logics;
• Performance evaluation, dependabilitymodeling, and analysis of real-time systems with different kinds oftimed Petri-Nets;
• Specification and analysis of communicationprotocols;
• Reliability, security, and dependability indistributed systems;
• Object orientation in distributed systemsarchitecture;
• Software development and concepts for distributedapplications;
• Computer network architecture and management;
• Language concepts for distributed systems.

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Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications. ... Read more

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A new foundation of Topology, summarized under the nameConvenient Topology, is considered such that several deficiencies oftopological and uniform spaces are remedied. This does not mean thatthese spaces are superfluous. It means exactly that a better frameworkfor handling problems of a topological nature is used. In this settingsemiuniform convergence spaces play an essential role. They includenot only convergence structures such as topological structures andlimit space structures, but also uniform convergence structures suchas uniform structures and uniform limit space structures, and they aresuitable for studying continuity, Cauchy continuity and uniformcontinuity as well as convergence structures in function spaces, e.g.simple convergence, continuous convergence and uniform convergence.Various interesting results are presented which cannot be obtained byusing topological or uniform spaces in the usual context. The text isself-contained with the exception of the last chapter, where theintuitive concept of nearness is incorporated in Convenient Topology(there exist already excellent expositions on nearness spaces).Audience: Students and mathematicians having some basicknowledge of topological spaces and seeking a deeper insight intopology on a convenient level will find this a valuable text. It isalso useful for researchers in the field of topology and itsapplications being interested in a further development of thepresented theory. ... Read more

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Arising from the 1996 Cape Town conference in honour of themathematician Bernhard Banaschewski, this collection of 30refereed papers represents current developments in category theory,topology, topos theory, universal algebra, model theory, and diverseordered and algebraic structures. Banaschewski's influence isreflected here, particularly in the contributions to pointfreetopology at the levels of nearness, uniformity, and asymmetry. Theunifying theme of the volume is the application of categoricalmethods. The contributing authors are: D. Baboolar, P.Bankston, R. Betti, D. Bourn, P. Cherenack,D. Dikranjan/H.-P. Künzi, X. Dong/W. Tholen, M.Erné, T.H. Fay, T.H. Fay/S.V. Joubert,D.N. Georgiou/B.K. Papadopoulos, K.A. Hardie/K.H.Kamps/R.W. Kieboom, H. Herrlich/A. Pultr, K.M.Hofmann, S.S. Hong/Y.K. Kim, J. Isbell, R.Jayewardene/O. Wyler, P. Johnstone, R. Lowen/P.Wuyts, E. Lowen-Colebunders/C. Verbeeck, R.Nailana, J. Picado, T. Plewe, J. Reinhold, G.Richter, H. Rörl, S.-H. Sun, Tozzi/V.Trnková, V. Valov/D. Vuma, and S. Veldsman.
Audience: This volume will be of interest to mathematicianswhose research involves category theory and its applications totopology, order, and algebra. ... Read more