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• That is to say, it is the Analogue of Space, not in the sense in which we formerly regarded Space as the negation of Matter; but in the sense of Infinite Dimensionality, or of Dimensionality in all directions, as a vague generalization from the three spatial dimensions Length, Breadth, and Thickness.
• This often happens, for example, when a two-dimensional solution is obtained for data whose appropriate dimensionality is higher.
• Finite Dimensionality of de Rham Cohomology:
• Proposition 5.3.1. If the manifold M has a finite good cover, then its cohomology is finite dimensional.
• As well as the low dimensionality of the Bloch electron states,[...]
• The difficulties in implementing classification algorithms as is, on high volume databases, derives from the increase in the number of records/instances in the database and of attributes/features in each instance (high dimensionality).
• The programming language does not impose any restrictions on the dimensionality of the arrays.
• A vector v=(22,38,52,12) defines a four-dimensional space with a point at the stated co-ordinates, and so on to any dimensionality n. Vector spaces of dimensionality greater than three are impossible to visualise directly[...]