Definition, Meaning, Synonyms & Anagrams | English word SEPARABLE

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Definitions of SEPARABLE

1. Able to be separated.
2. (analysis, of a topological space) Having a countable dense subset.
3. (mathematics, of a differential equation) Able to be brought to a form where all occurrences of the dependent and the independent variable are on opposite sides of the equal sign.

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Examples of Using SEPARABLE in a Sentence

• Bessel's equation arises when finding separable solutions to Laplace's equation and the Helmholtz equation in cylindrical or spherical coordinates.
• The aforementioned theorems do not preclude the state of one system becoming entangled with the state of another as cloning specifically refers to the creation of a separable state with identical factors.
• In the physical sciences, a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable.
• Separable algebra, a generalization to associative algebras of the notion of a separable field extension.
• In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset.
• A restricted form of the Baire category theorem, in which the complete metric space is also assumed to be separable, is provable in ZF with no additional choice principles.
• There are cases where the assumption of separable motion no longer holds, which make the approximation lose validity (it is said to "break down"), but even then the approximation is usually used as a starting point for more refined methods.
• The amount of freedom in that isomorphism is known as the Galois group of p (if we assume it is separable).
• If a field K contains a primitive n-th root of unity and the n-th root of an element of K is adjoined, the resulting Kummer extension is an abelian extension (if K has characteristic p we should say that p doesn't divide n, since otherwise this can fail even to be a separable extension).
• This follows from the previous result about completely metrizable subspaces and the fact that every subspace of a separable metric space is separable.
• The Atiyah-Jänich theorem identifies the K-theory K(X) of a compact topological space X with the set of homotopy classes of continuous maps from X to the space of Fredholm operators H→H, where H is the separable Hilbert space and the set of these operators carries the operator norm.
• In quantum mechanics, observables manifest as self-adjoint operators on a separable complex Hilbert space representing the quantum state space.
• The order also includes some gilled mushrooms, in the families Gomphidiaceae, Serpulaceae, Tapinellaceae, Hygrophoropsidaceae, and Paxillaceae, which often have the same flesh texture as the boletes, spore-bearing tissue which is also easily separable from the cap, and similar microscopic characteristics of spores and cystidia.
• A metric space is Lindelöf if and only if it is separable, and if and only if it is second-countable.
• It makes sense to consider all the long spaces at once because every connected (non-empty) one-dimensional (not necessarily separable) topological manifold possibly with boundary, is homeomorphic to either the circle, the closed interval, the open interval (real line), the half-open interval, the closed long ray, the open long ray, or the long line.
• These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix quantum groups (which are structures on unital separable C*-algebras), and bicrossproduct quantum groups.
• If an integrand can be rewritten in a form which is approximately separable this will increase the efficiency of integration with VEGAS.
• It presents the theory of dimension for separable metric spaces with what seems to be an impossible mixture of depth, clarity, precision, succinctness, and comprehensiveness.
• Then, if Q is separable (which is the case for every p but a finite number) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.
• A phrasal verb is written as two words that are analyzed semantically as a unit, but the unit may be separable under certain circumstances.

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