General Position - Abstractly: Configuration Spaces

Abstractly: Configuration Spaces

In very abstract terms, general position is a discussion of generic properties of a configuration space; in this context one means properties that hold on the generic point of a configuration space, or equivalently on a Zariski-open set.

This notion coincides with the measure theoretic notion of generic, meaning almost everywhere on the configuration space, or equivalently that points chosen at random will almost surely (with probability 1) be in general position.

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