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The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,mathsf d,mathfrak m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong mathrm {CD}^{*}(K,N) condition of Bacher-Sturm.

Metric spaces.

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Espaces publics. --- Public spaces.

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This monograph develops the theory of pre-Riesz spaces, which are the partially ordered vector spaces that embed order densely into Riesz spaces. Concepts from Riesz space theory such as disjointness, ideals, and bands are extended to pre-Riesz spaces. The analysis revolves around embedding techniques, including the Riesz completion and the functional representation. In the same spirit, norms and topologies on a pre-Riesz space and their extensions to the Riesz completion are examined. The generalized concepts are used to investigate disjointness preserving operators on pre-Riesz spaces and related notions. The monograph presents recent results as well as being an accessible introduction to the theory of partially ordered vector spaces and positive operators. Contents A primer on ordered vector spaces Embeddings, covers, and completions Seminorms on pre-Riesz spaces Disjointness, bands, and ideals in pre-Riesz spaces Operators on pre-Riesz spaces

Riesz spaces. --- Partially ordered spaces. --- Vector spaces. --- Linear spaces --- Linear vector spaces --- Algebras, Linear --- Functional analysis --- Vector analysis --- Spaces, Partially ordered --- Ordered topological spaces --- Topological spaces --- Riesz vector spaces --- Vector lattices --- Lattice theory --- Vector spaces

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This book is an ethnographic study by Ida Åberg that explores the phenomenon of urban gardening in Sweden, focusing on its role in public space. It examines the boundaries and implications of using urban areas for gardening, analyzing media, interviews, social media, and participant observations at urban gardens in Stockholm. The study is framed within post-structuralist discourse theory and critical geography, highlighting how urban gardens renegotiate property boundaries and create affective bonds that contribute to the positive discourse surrounding urban gardening. The work aims to understand how urban gardening can influence sustainable development and public space usage, targeting scholars and practitioners in urban studies and environmental policy.

Urban gardening. --- Public spaces. --- Urban gardening --- Public spaces

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Social cohesion is often perceived as being under threat from the increasing cultural and economic differences in contemporary cities and the increasing intensity of urban life. Public space, in its role as the main stage for social interactions between strangers, clearly plays a role in facilitating or limiting opportunities for social cohesion. But what exactly is social cohesion, how is it experienced in the public realm, and what role can the design of city spaces have in supporting or promoting it? There are significant knowledge gaps between the social sciences and design disciplines and between academia and practice, and thus a dispersed knowledge base that currently lacks nuanced insight into how urban design contributes to social integration or segregation. This book brings together scholarly knowledge at the intersection of public space design and social cohesion. It is based on original scholarly research and a depth of urban design practice, and analyses case studies from a variety of cities and cultures across the Global North and Global South. Its interdisciplinary, cross-cultural analysis will be of interest to academics, students, policymakers and practitioners engaged with a range of subject areas, including urban design, urban planning, architecture, landscape, cultural studies, human geography, social policy, sociology and anthropology. It will also have significant appeal to a wider non-academic readership, given its topical subject matter.

City planning. --- Public spaces --- Sociology, Urban. --- Design.