Categorical Structures And Their Applications: Proceedings Of The North-west European Category Seminar, Berlin, Germany 28 - 29 March 2003

The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich — one of the leading category theorists of the world — to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences 3. The Tensor Product......Page 10 Preface......Page 14 Introduction......Page 16 Opening Ceremony of the North-West European Category Seminar 2003......Page 18 On Boole's Booleanness B. Banaschewski......Page 24 References......Page 35 Introduction......Page 36 Nearness spaces and extensions of topological spaces......Page 37 Extensions of homeomorphisms......Page 42 Examples......Page 47 REFERENCES......Page 49 Introduction......Page 52 1. Orthomodular Posets......Page 53 2. Categorical Properties......Page 56 On a Weak Form of the Blumberg Property Wing-Sum Cheung, Yu-Ting Lin, George E. Strecker and Shiojenn Tseng......Page 63 2. The Weak Blumberg Property......Page 65 References......Page 72 Saturated Collections of Metrics E. Colebunders, R. Lowen and M. Sioen......Page 74 2. Preliminaries......Page 75 3. Saturation conditions......Page 76 4. Examples and counterexamples......Page 77 Bibliography......Page 87 A Uniform Space Proof of a Metrisation Theorem P. J. Collins......Page 90 References......Page 91 1. Introduction......Page 92 2. The large lattice of closure operators of Top and its subcategories......Page 94 3. Idenipotency, hereditariness and productivity......Page 96 4. Additivity and symmetry......Page 101 5. Testing the Sierpiriski space......Page 105 6. Testing the reals......Page 113 7. Characterization of the Kuratowski closure in smaller subcategories......Page 117 References......Page 120 1. Basic structures of monoidal predicate logics......Page 122 3. Relations between the basic structures......Page 124 4. t-Norms......Page 125 5. Interior operators of basic structures......Page 126 6. Examples of interior operators and closure operators defined by t-norms......Page 127 7. On modal logics......Page 133 References......Page 135 1. Introduction......Page 136 2. Separated affine sets and completions......Page 137 3. Internal characterization......Page 139 References......Page 142 0. Introduction......Page 144 2. Composition of cubical diagrams......Page 148 3. A twisted triple category......Page 151 4. The 2 x 2 properties......Page 157 5. The six snowflakes......Page 162 References......Page 164 Productivity of Coreflective Classes in Some Topological Structures......Page 166 1. Introduction......Page 167 2. Basic notions......Page 168 3. Topological spaces......Page 170 4. Uniform spaces......Page 171 5. Topological linear spaces......Page 172 6. Topological groups......Page 176 7. Summary......Page 178 References......Page 179 1. Introduction......Page 180 2. Structures......Page 181 3. Retracts of Structures......Page 188 4. Wreath Products......Page 192 References......Page 195 Maximal (Sequentially) Compact Topologies Hans-Peter A. Kiinzi and Dominic van der Zypen......Page 196 1. Introduction......Page 197 2. Main problem and related questions......Page 198 3. Some further results......Page 203 4. Sobriety and maximal compactness......Page 206 References......Page 209 1. Introduction......Page 212 3. Functorial Relationship between CEXT and SN......Page 213 4. Filterisotopic Spaces......Page 220 References......Page 228 1. Introduction......Page 230 2. Galois Connections and Lagois Connections......Page 231 3. Galois Correspondences and Lagois Correspondences......Page 235 References......Page 240 On (B,B)-Projectivity Helga Oltmanns, Valdis Laan, Ulrich Knauer......Page 242 1. (B, B)-projective right acts over monoids......Page 243 2. (B, B)-projectivity in categories......Page 245 3. Applications......Page 247 References......Page 249 On Coalgebras which are Algebras......Page 250 References......Page 258 0. Introduction......Page 260 1. Hyperspace structures for all semiuniform convergence spaces......Page 262 2. Hyperspace structures for semiuniform limit spaces......Page 268 References......Page 272 1. Introduction......Page 274 2. Ordered positively convex modules.......Page 276 3. Convex effect algebras and partially ordered cone modules.......Page 279 References......Page 287 0. Introduction......Page 288 1. Fibrewise Sobriety......Page 292 2. The Fibrewise Hofmann-Lawson-Theorem......Page 299 3. Exponentiable Fibrewise Sober Maps......Page 302 References......Page 305 Two Applications of Elementary Submodels to Partitions of Topological Spaces......Page 308 References......Page 311 Introduction......Page 314 1. Preliminaries: GL-rnonoids......Page 315 3. L-valued categories of L-sets......Page 316 4. L-valued categories related to algebra......Page 323 5. L-valued categories related to topology......Page 325 6. L-valued categories of proximity spaces......Page 329 7. L-valued categories related to topological algebra......Page 332 References......Page 333 B) Mathematical Biography......Page 336 C) Books......Page 337 Bernhard Banaschewski: Two Poems......Page 356 "The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich - one of the leading category theorists of the world - to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst Herrlich's publications."--BOOK JACKET