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100			_aHaridis, Alexandros _958282
245			_aThe topology of shapes made with points/
260			_bSage, _c2020.
300			_aVol. 47, Issue 7, 2020, ( 1279–1288 p.)
520			_aIn architecture, city planning, visual arts, and other design areas, shapes are often made with points, or with structural representations based on point-sets. Shapes made with points can be understood more generally as finite arrangements formed with elements (i.e. points) of the algebra of shapes Ui, for i = 0. This paper examines the kind of topology that is applicable to such shapes. From a mathematical standpoint, any “shape made with points” is equivalent to a finite space, so that topology on a shape made with points is no different than topology on a finite space: the study of topological structure naturally coincides with the study of preorder relations on the points of the shape. After establishing this fact, some connections between the topology of shapes made with points and the topology of “point-free” pictorial shapes (when i > 0) are defined and the main differences between the two are summarized.
773	0		_08876 _917104 _dLondon Pion Ltd. 2010 _tEnvironment and planning B: planning and design (Urban Analytics and City Science) _x1472-3417
856			_uhttps://doi.org/10.1177/2399808319827015
942			_2ddc _cEJR
999			_c14835 _d14835