Papers in Honour of Bernhard Banaschewski : Proceedings of the BB Fest 96, a Conference Held at the University of Cape Town, 15–20 July 1996, on Category Theory and Its Applications to Topology, Order and Algebra

Arising from the 1996 Cape Town conference in honour of the mathematician __Bernhard Banaschewski__, this collection of 30 refereed papers represents current developments in category theory, topology, topos theory, universal algebra, model theory, and diverse ordered and algebraic structures. Banaschewski's influence is reflected here, particularly in the contributions to pointfree topology at the levels of nearness, uniformity, and asymmetry. The unifying theme of the volume is the application of categorical methods. 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 mathematicians whose research involves category theory and its applications to topology, order, and algebra. Front Matter....Pages i-1 Relatively Parametrizable Subalgebras....Pages 3-6 An ‘Unsitely’ Result on Atomic Morphisms....Pages 7-15 Quotient Maps of Locales....Pages 17-44 Some Applications of the Ultrapower Theorem to the Theory of Compacta....Pages 45-66 Nearness, Subfitness and Sequential Regularity....Pages 67-80 The Structural Nature of the Nerve Functor for n -Groupoids....Pages 81-113 Prime Ideal Theory for General Algebras....Pages 115-144 An Illustration of the Power of Structure Theory....Pages 145-160 Coreflectivity of E-Monads and Algebraic Hulls....Pages 161-173 Separation and Epimorphisms in Quasi-Uniform Spaces....Pages 175-207 A Homotopy 2-Groupoid of a Hausdorff Space....Pages 209-234 A Complete Classification of the Simultaneously Bireflective and Bicoreflective Subconstructs of Approach Spaces....Pages 235-245 Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison....Pages 247-256 Completeness and Cocompleteness of R Smod 1N ....Pages 257-269 Cauchy Complete Nearness Spaces....Pages 271-277 Categories of Relations and Functional Relations....Pages 279-305 Weak Equivalence of Internal Categories....Pages 307-316 Isolated Submodules and Skew Fields....Pages 317-326 Clone Segments of the Tychonoff Modification of Space....Pages 327-337 Representation of Relations by Partial Maps....Pages 339-350 Structured Frames by Weil Entourages....Pages 351-366 Finite Intervals in the Lattice of Topologies....Pages 367-376 Local Connectedness Made Uniform....Pages 377-390 Frölicher versus Differential Spaces: A Prelude to Cosmology....Pages 391-413 Weakly Hereditary Initial Closure Operators....Pages 415-431 Strongly θ-Continuous Functions and Topologies on Function Spaces....Pages 433-444 (Strongly) Zero-Dimensional Partially Ordered Spaces....Pages 445-456 Structure Sheaves for Additive Categories....Pages 457-473 Lindelöf Degree and Function Spaces....Pages 475-483 Connectednesses and Disconnectednesses of Petri Nets....Pages 485-504 Arising from the 1996 Cape Town conference in honour of the mathematician Bernhard Banaschewski , this collection of 30 refereed papers represents current developments in category theory, topology, topos theory, universal algebra, model theory, and diverse ordered and algebraic structures. Banaschewski's influence is reflected here, particularly in the contributions to pointfree topology at the levels of nearness, uniformity, and asymmetry. The unifying theme of the volume is the application of categorical methods. 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 mathematicians whose research involves category theory and its applications to topology, order, and algebra. Proceedings of the BB Fest 96, a conference held at the University of Cape Town, 15-20 July 1996, on Category Theory and its Applications to Topology, Order and Algebra