Contents -- Preface -- Introduction -- Opening Ceremony of the North-West European Category Seminar 2003 -- On Boole's Booleanness B. Banaschewski -- References -- Homeomorphically Closed Nearness Spaces H. L. Bentley and John W. Carlson -- Introduction -- Nearness spaces and extensions of topological spaces -- Extensions of homeomorphisms -- Examples -- REFERENCES -- The Tensor Product of Orthomodular Posets Reinhard Borger -- Introduction -- 1. Orthomodular Posets -- 2. Categorical Properties -- 3. The Tensor Product -- References -- On a Weak Form of the Blumberg Property Wing-Sum Cheung, Yu-Ting Lin, George E. Strecker and Shiojenn Tseng -- 1. Introduction -- 2. The Weak Blumberg Property -- References -- Saturated Collections of Metrics E. Colebunders, R. Lowen and M. Sioen -- 1. Introduction -- 2. Preliminaries -- 3. Saturation conditions -- 4. Examples and counterexamples -- Bibliography -- A Uniform Space Proof of a Metrisation Theorem P. J. Collins -- References -- Classification of Closure Operators for Categories of Topological Spaces Dikran Dikranjan, Walter Tholen and Stephen Watson -- 1. Introduction -- 2. The large lattice of closure operators of Top and its subcategories -- 3. Idenipotency, hereditariness and productivity -- 4. Additivity and symmetry -- 5. Testing the Sierpiriski space -- 6. Testing the reals -- 7. Characterization of the Kuratowski closure in smaller subcategories -- References -- Topological Structures in Logics Werner Gahler -- 1. Basic structures of monoidal predicate logics -- 2. Associated monoidal predicate logics -- 3. Relations between the basic structures -- 4. t-Norms -- 5. Interior operators of basic structures -- 6. Examples of interior operators and closure operators defined by t-norms -- 7. On modal logics -- References -- The Structure of Affine Algebraic Sets Eraldo Giuli -- 1. Introduction.

2. Separated affine sets and completions -- 3. Internal characterization -- References -- A Twisted Triple Category of Track Commutative Cubes K. A. Hardie and K. H. Kamps -- 0. Introduction -- 2. Composition of cubical diagrams -- 3. A twisted triple category -- 4. The 2 x 2 properties -- 5. The six snowflakes -- References -- Productivity of Coreflective Classes in Some Topological Structures -- 1. Introduction -- 2. Basic notions -- 3. Topological spaces -- 4. Uniform spaces -- 5. Topological linear spaces -- 6. Topological groups -- 7. Summary -- References -- A Characterization of Co-Retracts of Functional Structures -- 1. Introduction -- 2. Structures -- 3. Retracts of Structures -- 4. Wreath Products -- References -- Maximal (Sequentially) Compact Topologies Hans-Peter A. Kiinzi and Dominic van der Zypen -- 1. Introduction -- 2. Main problem and related questions -- 3. Some further results -- 4. Sobriety and maximal compactness -- References -- Supertopologies as Starting Points for Generalized Continuity Structures -- 1. Introduction -- 2. Super near Spaces -- 3. Functorial Relationship between CEXT and SN -- 4. Filterisotopic Spaces -- References -- Introducing Lagois Correspondences -- 1. Introduction -- 2. Galois Connections and Lagois Connections -- 3. Galois Correspondences and Lagois Correspondences -- References -- On (B,B)-Projectivity Helga Oltmanns, Valdis Laan, Ulrich Knauer -- 1. (B, B)-projective right acts over monoids -- 2. (B, B)-projectivity in categories -- 3. Applications -- References -- On Coalgebras which are Algebras -- References -- A Hyperspace Completion for Semiuniform Convergence Spaces and Related Hyperspace Structures -- 0. Introduction -- 1. Hyperspace structures for all semiuniform convergence spaces -- 2. Hyperspace structures for semiuniform limit spaces -- References.

Convex Effect Algebras and Partially Ordered Positively Convex Modules -- 1. Introduction -- 2. Ordered positively convex modules. -- 3. Convex effect algebras and partially ordered cone modules. -- References -- Fibrewise Sobriety -- 0. Introduction -- 1. Fibrewise Sobriety -- 2. The Fibrewise Hofmann-Lawson-Theorem -- 3. Exponentiable Fibrewise Sober Maps -- References -- Two Applications of Elementary Submodels to Partitions of Topological Spaces -- References -- L-Valued Categories: Generalities and Examples Related to Algebra and Topology -- Introduction -- 1. Preliminaries: GL-rnonoids -- 2. L-valued categories: basic concepts -- 3. L-valued categories of L-sets -- 4. L-valued categories related to algebra -- 5. L-valued categories related to topology -- 6. L-valued categories of proximity spaces -- 7. L-valued categories related to topological algebra -- References -- Horst Herrlich's Publications -- A) As Editor -- B) Mathematical Biography -- C) Books -- D) Papers -- Bernhard Banaschewski: Two Poems.