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Page "Compact space" ¶ 7
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Specifically and topological
Specifically, a function between measurable spaces is said to be measurable if the preimage of each measurable set is measurable, analogous to the situation of continuous functions between topological spaces.
Specifically, if X and Y are pointed spaces ( i. e. topological spaces with distinguished basepoints x < sub > 0 </ sub > and y < sub > 0 </ sub >) the wedge sum of X and Y is the quotient of the disjoint union of X and Y by the identification x < sub > 0 </ sub > ∼ y < sub > 0 </ sub >:
Specifically, curvature ( the gravitational field ) might arise as a kind of " averaging " over very complicated topological phenomena at very small scales, the so-called spacetime foam.
Specifically, a topological space X is compactly generated if it satisfies the following condition:
Specifically, let X and Y be a topological spaces with A a subspace of Y.
Specifically, a pseudogroup on a topological space S is a collection Γ of homeomorphisms between open subsets of S satisfying the following properties.
Specifically, a Montel space is a barrelled topological vector space where every closed and bounded set is compact.

Specifically and space
Specifically, the left invariant extension of an element v of the tangent space at the identity is the vector field defined by v ^< sub > g </ sub > =
Specifically, spinors are objects associated to a vector space with a quadratic form ( like Euclidean space with the standard metric or Minkowski space with the Lorentz metric ), and are realized as elements of representation spaces of Clifford algebras.
Specifically, if F is a vector space of linear functionals on X which separates points of X, then the continuous dual of X with respect to the topology σ ( X, F ) is precisely equal to F.
Specifically, a Clifford algebra is a unital associative algebra which contains and is generated by a vector space V equipped with a quadratic form Q.
( Specifically, a thin space is endorsed for typesetting ; a regular word space is sufficient wherever typographical nicety is impractical.
Specifically, f (' F ', ' F ', ..., ' F ') = ' F ', and these functions correspond to linear maps over the Boolean vector space.
Specifically, the linear span of the basis must be dense in H, but it may not be the entire space.
Specifically, a space velocity along the line-of-sight means that the transformation from tangential linear velocity to ( angular ) proper motion is a function of time.
Specifically, the similarity between the fiber bundle E and a product space B × F is defined using a continuous surjective map
Specifically, the scalar curvature represents the amount by which the volume of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.
Specifically, if a system is in a state described by a vector in a Hilbert space, the measurement process affects the state in a non-deterministic, but statistically predictable way.
Specifically, if X is a 1-dimensional CW-complex, the attaching map for a 1-cell is a map from a two-point space to X,.
Specifically, it is focussed on military, medical, aerospace, space and automotive markets.
Specifically, it shows that if M is a unital, self-adjoint operator algebra in the C *- algebra B ( H ), for some Hilbert space H, then the weak closure, strong closure and bicommutant of M are equal.
Specifically, it must meet less than two of the five Hugo criteria for consideration as a semiprozine: that the magazine had an average press run of at least one thousand copies per issue, paid its contributors and / or staff in other than copies of the publication, provided at least half the income of any one person, had at least fifteen percent of its total space occupied by advertising, and announced itself to be a semiprozine.
Specifically, experiments will study the adaptation of the vestibular system and space adaptation syndrome, the adaptation of the central nervous system and the pathways which control the ability to sense location in the absence of gravity, and the effect of microgravity on a developing nervous system.
Specifically, let X be a separable normed space and B the closed unit ball in X < sup >∗</ sup >.
Specifically, Fock showed that the Schrödinger wavefunction in the momentum space for the Kepler problem was the stereographic projection of the spherical harmonics on the sphere.

Specifically and is
Specifically, in quantum mechanics, the state of an atom, i. e. an eigenstate of the atomic Hamiltonian, is approximated by an expansion ( see configuration interaction expansion and basis set ) into linear combinations of anti-symmetrized products ( Slater determinants ) of one-electron functions.
Specifically, is the neuter plural of, an adjective related to the verb ἀποκρύπτω ἀποκρύπτειν ( apocriptein ), " to hide something away.
Specifically, at speeds of OC-3 and above, the cost of segmentation and reassembly ( SAR ) hardware makes ATM less competitive for IP than Packet Over SONET ( POS ); because of its fixed 48-byte cell payload, ATM is not suitable as a data link layer directly underlying IP ( without the need for SAR at the data link level ) since the OSI layer on which IP operates must provide a maximum transmission unit ( MTU ) of at least 576 bytes.
* Specifically, a text added to the end of a book or an article, containing information that is important to, but is not the main idea of, the main text
Specifically, in one of his last works, De scientia divina, he concludes that the idea of plurality itself is strictly temporal, a human notion.
Specifically, if A is a linear operator and is a bra, then is another bra defined by the rule
Specifically it is the amount of a substance that contains as many elementary entities ( atoms, molecules or ions ) as there are atoms in 0. 012 kilogram ( or 12 grams ) of carbon-12, where the carbon-12 atoms are unbound, at rest and in their ground state.
Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.
Specifically, after acknowledging the various popular theories in vogue at the time, of how atoms were reasoned to attach to each other, i. e. " hooked atoms ", " glued together by rest ", or " stuck together by conspiring motions ", Newton states that he would rather infer from their cohesion, that " particles attract one another by some force, which in immediate contact is exceedingly strong, at small distances performs the chemical operations, and reaches not far from the particles with any sensible effect.
Specifically, to minimize the cutting down of trees for fuel, kerosene is being subsidized, and efforts are being made to replace the loss of the forest cover caused by ylang-ylang distillation for perfume.
Specifically, the timescale for beta-decay of radioactive nuclei produced is faster than the timescale for fusion.
Specifically, if p is the natural length of a section of spring, then the length of the spring with tension T applied has length
Specifically, if one or more of the produced neutrons themselves interact with other fissionable nuclei, and these also undergo fission, then there is a possibility that the macroscopic overall fission reaction will not stop, but continue throughout the reaction material.
Specifically, the table provides conflicting answers to the question of what this particular employee's address is.
Specifically, if he / she chooses to determine the path, then he / she has no influence whatsoever over which of the two paths, the left one or the right one, nature will tell him / her is the one in which the particle is found.
Specifically, it is a non-trivial ring in which every non-zero element a has a multiplicative inverse, i. e., an element x with.
Specifically, it is a vector field.
Specifically, it is claimed that Ezekiel himself may have suffered from temporal lobe epilepsy, which has several characteristic symptoms that are apparent from his writing.
Specifically, by the Casorati – Weierstrass theorem, for any transcendental entire function f and any complex w there is a sequence with, is necessarily a polynomial, of degree at least n.

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