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The two-dimensional Euclidean space denoted R^2.

The continuous image of a Polish space, also called an analytic set.

A topological space is second countable if it has a countable topological basis.

A complete metric is a metric in which every Cauchy sequence is convergent. A topological space with a complete metric is called a complete metric space.

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.

A graded algebra over the integers Z. Cohomology of a space is a graded ring.

A smooth manifold with a Poisson bracket defined on its function space.

Consider a probability space specified by the triple (S,S,P), where (S,S) is a measurable space, with S the domain and S is its measurable subsets, and P is a measure on S ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...