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- W962792992 abstract "abstractive class any totally ordered class G of regions such that i ) G is totally ordered ii ) no region exists which is contained in all the regions in G . We denote by AC the set of abstractive classes. The idea is that an abstractive class represents an “abstract object” which is the limit (the intersection, in a sense) of the regions in the abstractive class. Condition ii ) means that these objects have a dimension lower than the one of the regions. As an example, in the canonical Euclidean plane an abstrac-tive class is intended to represent either a point or a line. Now, it is possible that two different abstractive classes represent the same object. For example, let G 1 be the class of closed balls with centre in P and let G 2 be the class of closed squares with the same centre. Then while G 1 ≠ G 2 , our intuition says that both G 1 and G 2 represent P . To face such a question, we define a pre-order relation and a corresponding equivalence relation. Definition 4.2. The covering" @default.
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- W962792992 date "2008-12-31" @default.
- W962792992 modified "2023-09-23" @default.
- W962792992 title "Mathematical Features of Whitehead’s Point-free Geometry" @default.
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