Geometrical Aspects Of Abstract Spaces

2007 ◽  
pp. 305-354
Keyword(s):  
Abstract Spaces

scholarly journals “The street is ours”. A comparative analysis of street trading, Covid-19 and new street geographies in Harare, Zimbabwe and Kisumu, Kenya

Food Security ◽  
2021 ◽  
Author(s):  
Richard Kiaka ◽  
Shiela Chikulo ◽  
Sacha Slootheer ◽  
Paul Hebinck
Keyword(s):  
Public Space ◽  
Urban Space ◽  
Street Vendors ◽  
Urban Food Security ◽  
Street Trading ◽  
Food Economy ◽  
City State ◽  
Abstract Spaces ◽  
The Impact ◽  
The City

AbstractThis collaborative and comparative paper deals with the impact of Covid-19 on the use and governance of public space and street trade in particular in two major African cities. The importance of street trading for urban food security and urban-based livelihoods is beyond dispute. Trading on the streets does, however, not occur in neutral or abstract spaces, but rather in lived-in and contested spaces, governed by what is referred to as ‘street geographies’, evoking outbreaks of violence and repression. Vendors are subjected to the politics of municipalities and the state to modernize the socio-spatial ordering of the city and the urban food economy through restructuring, regulating, and restricting street vending. Street vendors are harassed, streets are swept clean, and hygiene standards imposed. We argue here that the everyday struggle for the street has intensified since and during the Covid-19 pandemic. Mobility and the use of urban space either being restricted by the city-state or being defended and opened up by street traders, is common to the situation in Harare and Kisumu. Covid-19, we pose, redefines, and creates ‘new’ street geographies. These geographies pivot on agency and creativity employed by street trade actors while navigating the lockdown measures imposed by state actors. Traders navigate the space or room for manoeuvre they create for themselves, but this space unfolds only temporarily, opens for a few only and closes for most of the street traders who become more uncertain and vulnerable than ever before, irrespective of whether they are licensed, paying rents for vending stalls to the city, or ‘illegally’ vending on the street.

scholarly journals Logical metatheorems for abstract spaces axiomatized in positive bounded logic

2016 ◽  
Vol 290 ◽  
pp. 503-551 ◽  
Author(s):  
Daniel Günzel ◽  
Ulrich Kohlenbach
Keyword(s):  
Abstract Spaces

Nonlinear Integral Equations in Abstract Spaces

1996 ◽  
Author(s):  
Dajun Guo ◽  
V. Lakshmikantham ◽  
Xinzhi Liu
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equations ◽  
Abstract Spaces

Vectors in ℝ n . Abstract spaces

1999 ◽  
pp. 117-122
Author(s):  
Knut Sydsæter ◽  
Arne Strøm ◽  
Peter Berck
Keyword(s):  
Abstract Spaces

New Tauberian Theorems from Old

1994 ◽  
Vol 46 (2) ◽  
pp. 380-394
Author(s):  
Mangalam R. Parameswaran
Keyword(s):  
Absolute Summability ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Tauberian Conditions ◽  
Powerful Approach ◽  
Abstract Spaces

AbstractA new and very general and simple, yet powerful approach is introduced for obtaining new Tauberian theorems for a summability method V from known Tauberian conditions for V, where V is merely assumed to be linear and conservative. The technique yields the known theorems on the weakening of Tauberian conditions due to Meyer-König and Tietz and others and also improves many of them. Several new results are also obtained, even for classical methods of summability, including analogues of Tauber's second theorem for the Borel and logarithmic methods. The approach yields also new Tauberian conditions for the passage from summability by a method V to summability by a method V', as well as to more general methods of summability like absolute summability or summability in abstract spaces; the present paper however confines itself to ordinary summability.

Special Section: Topological representation and reasoning in design and manufacturing

2000 ◽  
Vol 14 (5) ◽  
pp. 355-358 ◽  
Author(s):  
DAN BRAHA
Keyword(s):  
Euclidean Plane ◽  
Special Section ◽  
Point Of View ◽  
Topological Methods ◽  
Geometric Objects ◽  
Design And Manufacturing ◽  
Mechanical Devices ◽  
Abstract Spaces ◽  
Modern Mathematics ◽  
Complex Activities

The word “topology” is derived from the Greek word “τοπος,” which means “position” or “location.” A simplified and thus partial definition has often been used (Croom, 1989, page 2): “topology deals with geometric properties which are dependent only upon the relative positions of the components of figures and not upon such concepts as length, size, and magnitude.” Topology deals with those properties of an object that remain invariant under continuous transformations (specifically bending, stretching, and squeezing, but not breaking or tearing). Topological notions and methods have illuminated and clarified basic structural concepts in diverse branches of modern mathematics. However, the influence of topology extends to almost every other discipline that formerly was not considered amenable to mathematical handling. For example, topology supports design and representation of mechanical devices, communication and transportation networks, topographic maps, and planning and controlling of complex activities. In addition, aspects of topology are closely related to symbolic logic, which forms the foundation of artificial intelligence. In the same way that the Euclidean plane satisfies certain axioms or postulates, it can be shown that certain abstract spaces—where the relations of points to sets and continuity of functions are important—have definite properties that can be analyzed without examining these spaces individually. By approaching engineering design from this abstract point of view, it is possible to use topological methods to study collections of geometric objects or collections of entities that are of concern in design analysis or synthesis. These collections of objects and or entities can be treated as spaces, and the elements in them as points.

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