Contents 1. Introduction 2 1.1. The general strategy: the cross-ratio method 2 1.2. Two sample calculations 7 1.3. Notation and Terminology 14 1.4. Summary of results 15 2. Degenerations of rational curves 17 2.1. The basic setup 17 2.2. The main results from deformation theory 20 2.3. The geometry of the Severi varieties 21 2.4. Singularities of the total space 37 3. Formulas 56 3.

The conceptual spaces approach has recently emerged as a novel account of concepts. Its guiding idea is that concepts can be represented geometrically, by means of metrical spaces. While it is generally recognized that many of our concepts are vague, the question of how to model vagueness in the conceptual spaces approach has not been addressed so far, even though the answer is far from straigh...

Introduction 1 1. Bundles 2 1.1. Pullback 2 1.2. Sections 3 1.3. Fiber bundles as fibrations 4 2. Vector bundles 4 2.1. Whitney sum 5 2.2. Sections of vector bundles 6 2.3. Inner products 6 3. Principal Bundles 7 3.1. Morphisms 7 3.2. Sections and trivializations 8 3.3. Associated bundles 9 3.4. Homotopy classification 11 3.5. B as a functor 14 4. Characteristic classes 16 4.1. Line Bundles 16 ...

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Given two Banach function spaces we study the pointwise product space E · F , especially for the case that the pointwise product of their unit balls is again convex. We then give conditions on when the pointwise product E ·M(E,F ) = F , where M(E,F ) denotes the space of multiplication operators from E into F .

In this note, we show that if a Banach space X has a predual, then every bounded linear operator on X with a continuous functional calculus admits a bounded Borel functional calculus. A consequence of this is that on such a Banach space, the classes of finitely spectral and prespectral operators coincide. We also apply this result to give some sufficient conditions for an operator with an absol...

For 0 < p < 1 we give examples of Banach spaces isometrically embedding into Lp but not into any Lr with p < r ≤ 1.

The conceptual spaces approach has emerged as a new and powerful way of thinking about concepts. In earlier work, the present authors have addressed the question of how to model vague concepts in the conceptual spaces framework. That in turn was instrumental in Decock’s and Douven’s account of a graded membership relation in further work. In this paper, we make use of the account of graded memb...

A careful analysis of the original definition of formal topology led to the introduction of a new primitive, namely a positivity relation between elements and subsets. This is, in other terms, a direct intuitionistic treatment of the notion of closed subset in formal topology. However, since formal open subsets do not determine formal closed subsets uniquely, the new concept of positivity relat...

In contemporary urban development, to improve the quality of public urban spaces has become one of the most outstanding goals of local urban policies, in order to increase pedestrian activities and people’s social interaction. In this context, to promote outdoor thermal comfort has an utmost importance, especially considering the heat island phenomenon. This paper recalls the use of urban desig...