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- W3099462005 abstract "In 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 $U_i$, 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 discussed and the main differences between the two are summarized." @default.
- W3099462005 created "2020-11-23" @default.
- W3099462005 creator A5052059685 @default.
- W3099462005 date "2019-02-11" @default.
- W3099462005 modified "2023-09-25" @default.
- W3099462005 title "The topology of shapes made with points" @default.
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- W3099462005 doi "https://doi.org/10.1177/2399808319827015" @default.
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