# compactness

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**Noetherian topological space**— In mathematics, a Noetherian topological space is a topological space in which closed subsets satisfy the descending chain condition. Equivalently, we could say that the open subsets satisfy the ascending chain condition, since they are the… …72

**Spectral theory of compact operators**— In functional analysis, compact operators are linear operators that map bounded sets to precompact ones. Compact operators acting on a Hilbert space H is the closure of finite rank operators in the uniform operator topology. In general, operators …73

**Prokhorov's theorem**— In mathematics, Prokhorov s theorem is a theorem of measure theory that relates tightness of measures to weak compactness (and hence weak convergence) in the space of probability measures. It is credited to the Soviet mathematician Yuri… …74

**Generalised metric**— In mathematics, the concept of a generalised metric is a generalisation of that of a metric, in which the distance is not a real number but taken from an arbitrary ordered field.In general, when we define metric space the distance function is… …75

**Curtis–Hedlund–Lyndon theorem**— The Curtis–Hedlund–Lyndon theorem is a mathematical characterization of cellular automata in terms of their symbolic dynamics. It is named after Morton L. Curtis, Gustav A. Hedlund, and Roger Lyndon; in his 1969 paper stating the theorem, Hedlund …76

**locomotion**— /loh keuh moh sheuhn/, n. the act or power of moving from place to place. [1640 50; see LOCOMOTIVE, MOTION] * * * Any of various animal movements that result in progression from one place to another. Locomotion is classified as either… …77

**density**— I (New American Roget s College Thesaurus) Compactness Nouns 1. density, denseness, solidity, solidness; impenetrability, impermeability; incompressibility; imporosity; cohesion (see coherence); constipation; consistency, spissitude; specific… …78

**Solidity**— So*lid i*ty, n. [L. soliditas: cf. F. solidit[ e].] 1. The state or quality of being solid; density; consistency, opposed to {fluidity}; compactness; fullness of matter, opposed to {openness} or {hollowness}; strength; soundness, opposed to… …79

**Brouwer fixed point theorem**— In mathematics, the Brouwer fixed point theorem is an important fixed point theorem that applies to finite dimensional spaces and which forms the basis for several general fixed point theorems. It is named after Dutch mathematician L. E. J.… …80

**Hausdorff space**— In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space …