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Analytical spaces --- Banach spaces.

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This book can be viewed as a bridge between the study of metric spaces and general topological spaces. About half the book is devoted to relatively little-known results, many of which are published here for the first time. The author sketches a theory of uniform transformation groups, leading to the theory of uniform spaces over a base and hence to the theory of uniform covering spaces.

Uniform spaces --- Uniform spaces.

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Absolute measurable space and absolute null space are very old topological notions, developed from well-known facts of descriptive set theory, topology, Borel measure theory and analysis. This monograph systematically develops and returns to the topological and geometrical origins of these notions. Motivating the development of the exposition are the action of the group of homeomorphisms of a space on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures on the unit cube, and the extensions of this theorem to many other topological spaces. Existence of uncountable absolute null space, extension of the Purves theorem and recent advances on homeomorphic Borel probability measures on the Cantor space, are among the many topics discussed. A brief discussion of set-theoretic results on absolute null space is given, and a four-part appendix aids the reader with topological dimension theory, Hausdorff measure and Hausdorff dimension, and geometric measure theory.

Topological spaces. --- Spaces, Topological

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Faisant appel aux neurosciences, l'auteur questionne ici l'importance de notre sensibilité dans la relation aux lieux. Quel lien existe-t-il entre les espaces et notre ressenti de bien-être ? Pour y répondre, l'auteur s'est penché sur la relation charnelle et affective des Parisiens à cinq lieux : le quai du RER B de Châtelet les Halles, le quartier de la Huchette, la rue Lagrange, le quartier des Peupliers et la place Pinel. Des pistes pour construire une autre ville durable, loin de tout bilan carbone, mais en incorporant notre nature sensible sont lancées ici.

Open spaces. --- Public spaces.

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This thesis by Lukáš Malý presents a study of Newtonian spaces based on quasi-Banach function lattices. It includes two papers that explore the generalization of Sobolev spaces in abstract metric measure spaces. The work discusses weak derivatives, weak upper gradients, and the techniques available for analyzing these spaces. It also covers the absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces. The thesis aims to broaden the theory of Newtonian spaces, making it applicable to more general metric spaces.

Sobolev spaces. --- Metric spaces.