Espaço abstrato e espaço diferencial: a compreensão do direito à cidade em Henri Lefebvre / Abstract and differential spaces: keys to understanding the right to the city in Henti Lefebvre

ResumoO presente trabalho possui o objetivo de fornecer uma visão panorâmica acerca das ancoragens teóricas da noção de direito à cidade, enquanto projeto orientador de uma hipótese virtual e possível, definida como sociedade urbana. Para tanto, através da revisão bibliográfica, recorre-se à reflexão acerca de alguns elementos, cuja análise se mostra fundamental para a delimitação do campo teórico em que o pensamento se constrói, na obra de Henri Lefebvre, especialmente no que concerne às categorias espaço abstrato e espaço diferencial. Conclui-se que a partir do estudo da obra de Lefebvre que o direito a cidade se constitui em um espaço de investigação onde é possível pensar os processos históricos assumidos em diferentes escalas até chegar a atualidade. Deste modo, o direito à cidade é adequado e objetiva fundir os conflitos e os processos urbanos com a produção do conhecimento socioespacial, permitindo a transformação do saber e da realidade da urbe.Palavras-chave: Henri Lefebvre; direito à cidade; sociedade urbana; espaço abstrato; espaço diferencial. AbstractThis article aims to provide a different angle of view about the theoretical anchors of the original notion of the right to the city, in Henri Lefebvre. Therefore, through literature review, of a qualitative-exploratory character, a dialectical reflection about the characteristics of the right to the city project is used, from the perspective of the spatial theory developed by the author at a later point in his work. Within this scope, and for the purposes of this study, the notions of “abstract space” and “differential space” were especially taken as analytical categories. In constant mobilization, these phenomena interact dialectically, and constitute the fundamental antithesis between domination and appropriation of the city, whose scan is promising for a particular understanding of the theoretical field in which the project of the right to the city is built on the work of Lefebvre. This analysis results in the understanding of the right to the city as a claim, which is established in the conflictive dialectic between two socio-spatial segments, present since the modern city: the abstract space, where the reason of State, the law and the capitalist ideology are allied in the project of homogenization of the society, and the differential space, founded on social relations rooted in the forms of using spaces that express ways of life that are resistant to the logic of capital.Keywords: Henri Lefebvre; right to the city; urban society; abstract space; differential space.

Some algebraic aspects of the gluing of differential spaces

The aim of this paper is to study the algebraic aspects of the gluing procedure in the category of differential spaces. In particular, the Sikorski differential spaces are studied. The algebraic techniques are mainly based on the spectral approach. This paper is a continuation of some previous researches in differential spaces techniques.

THE PEOPLE’S BOUROUGH PLAN OF ACTION: A COUNTER-PROJECT OF INSURGENT CITIZENSHIP1

ABSTRACT Porto Alegre is divided in eight Boroughs of Planning. Each Borough has a representative in the Urban Planning City Council (UPCC). In 2018 social movements organized to conquer this. From this, some of the Boroughs’ councilors felt the need to better inform themselves on the terms and subjects discussed in the UPCC, and to ensure that their local issues would be discussed. For that manner, the People’s Borough Plan of Action (PBPA) project was created by a coalition of social movements, the architect’s association (IAB-RS) and the university to perform counter-hegemonic actions. The project is based on the insurgent planning theory, which understands urban development from the standpoint of the global south as being essentially performed by communities, activists and grassroots strategies. Thus, the project moves across both invited and invented spaces of action in a non-binary relationship, with the aim of providing the grassroots movements of insurgent citizenship with technical assistance to support their claims and desires over the city they live. Regarding the City’s Master Plan revision, the PBAP represents a counter-plan related to the creation of differential spaces. Therefore, they create a moment of realization of the right to the city.

Menuju Urbanisasi Pulau Kecil: Produksi Ruang Abstrak dan Perampasan

<p class="ISI-Paragraf"><span lang="EN-US">Agrarian conflict in Pari Island of Seribu Islands, Jakarta has been undergoing for more than twenty years. The conflict involves main parties, in which the locals are diametrically opposed to local government-backed tourist corporations. This inductive qualitative study explores the historical information of the conflict and constructs a theoretical proposition at the mezzo level concerning the cause of this conflict by using an analytical tool from Lefebvre's concept of "production of space" and "accumulation by dispossession" by Harvey. The purpose of this study is to obtain a theoretical explanation at the intermediate level on the relation between abstract space production, dispossession and rural urbanization in favor of the tourism industry. The result shows, the production of abstract spaces, dispossession and urbanization located in a linear path for the production of capital space that turn social space into a space of capital accumulation, transforms agrarian resources into commodities and creates landless free labor for the future modern tourist industry. This study also shows that imbalanced contestation of spatial conflicts in Pari Island potentially marginalize local communities, furthermore, converting insular space into exclusively private-based industries is inappropriate because corporation has geographically expansive tendencies. Thus, policy makers are advised to support the life of differential spaces so that the diversity and particularity that exist in Pari Island can live together. It is this action that will overcome the damage caused by the production of abstract spaces and dispossession in the past and become the solution to the agrarian conflict in Pari Island.</span></p>

On b-boundary in differential spaces category

The aim of this paper is to present a new conceptual approach towards the well-known Schmidt's b-boundary of spacetime. Instead of working in the category of infinitely differentiable manifolds (called also smooth manifolds), we switch to the category of Sikorski differential spaces. Yet, such an approach was developed some time ago, but in this paper, we develop it further. In particular, we mix it with algebraic approach á la Nestruev. It lead us in a natural way towards the new concept of so called generator boundary (in short: gen-boundary). Surprisingly, such a study in the context of cosmology has not been done yet. We provide a through explanation of jointed Nestruev and Sikorski's formalisms. Further, as a result, the concept of gen-boundary emerges. We discuss its properties. Afterwards, having the developed techniques at hand, we re-discuss the Schmidt's b-boundary in this new (more algebraic) language. Interestingly, a classification of spacetime singularities naturally emerges from the proposed formalism.

The reproduction of rural spaces through education: Abstraction of the rural and the creation of new differential spaces

This paper examines the situating of rural communities in the United States within the neoliberal global context. It will focus on Henri Lefebvre's concept of abstract space, as well as additional theories on the ways space is produced and understood. The paper will use these theories to create an understanding of the ways rural communities are shaped and the role education plays in reproducing neoliberal ideology specifically through rural school consolidation. Abstracted rural space and schools are leading rural youth to internalize neoliberal ideology wherein they see themselves as economic actors rather than active engaged members of their community, and the best way to be successful is to gain the mobility to move to an urban center. Under this line of thought, rural exists only to serve capital as a site of resource extraction and low wage labor. The paper will conclude with a discussion on the way rural education can provide rural youth with the knowledge in which to produce rural spaces that represent what a modern rural community should be, focusing on improving the quality of life for residents, rather than what neoliberal capitalism needs it to be through the creation of common schools. This type of education can lead to the development of a right to the rural, a play off of Lefebvre's right to the city, wherein rural youth can critically examine their place and the place of rural communities in the world.