- Types:
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subspace
a space that is contained within another space
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null space
a space that contains no points; and empty space
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manifold
a set of points such as those of a closed surface or an analogue in three or more dimensions
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metric space
a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality
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Euclidean space
a space in which Euclid's axioms and definitions apply; a metric space that is linear and finite-dimensional
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Hilbert space
a metric space that is linear and complete and (usually) infinite-dimensional