A hyperoperation (*) on a non-empty set H is a mapping from H x H to power set P *( H ) ( the set of all non-empty sets of H ), i. e.

*( BCT1 ) Every complete metric space is a Baire space.

*( BCT1 ) Every complete metric space is a Baire space.

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For any topological space X, let C ( X ) denote the family of real-valued continuous functions on X and let C *( X ) be the subset of bounded real-valued continuous functions.

* A space X is completely regular if and only if it has the initial topology induced by C ( X ) or C *( X ).

*( BCT2 ) Every locally compact Hausdorff space is a Baire space.

Here y *( w ) denotes the value of the linear functional y * ( which is an element of the dual space of W ) when evaluated at the element w ∈ W. This scalar in turn is multiplied by x to give as the final result an element of the space V.

*( BCT2 ) Every locally compact Hausdorff space is a Baire space.

*( a ) is a finite-dimensional k-vector space for any p.

The prime mechanism then appeared to be this: Given a space X carrying a vector bundle, that implied in the homotopy category a mapping from X to a classifying space BG, for the relevant linear group G. For the homotopy theory the relevant information is carried by compact subgroups such as the orthogonal groups and unitary groups of G. Once the cohomology H *( BG ) was calculated, once and for all, the contravariance property of cohomology meant that characteristic classes for the bundle would be defined in H *( X ) in the same dimensions.

*( c ) Promote University integration into the European space as well as creation of the curricula, study and research programs, cooperation between University institutions, mobility and integrated teaching ;

*( V, x ) where x is a value of unspecified nature ; and

A group is of characteristic 2 type if the generalized Fitting subgroup F *( Y ) of every 2-local subgroup Y is a 2-group.

*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

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Then the probability density function f *( x ) of the size biased population is

Completely regular spaces can be characterized by the fact that their topology is completely determined by C ( X ) or C *( X ).

*( plant ) Amaranthus retroflexus L. – " L ." is the standard abbreviation for " Linnaeus "; the absence of parentheses shows that this is his original name.

*( with Nicholas Cohen ), The growth of hunger: a new politics of agriculture, London: Boyars, 1980-This book is based on René Dumont ’ s ideas as contained in the 1975 publ.

In other words, if a planet, M, follows an elliptical orbit around a focus F and has a point P where PM is tangent to the curve and FPM is a right angle so that FP is the perpendicular to the tangent, then the centripetal force at point P is proportional to F * M /( R *( F * P )< sup > 3 </ sup >) where R is the radius of the curvature at M. Johann Bernoulli proved this formula in 1710.

*( A < sub > 1 </ sub > ⊕ ··· ⊕ A < sub > n </ sub >, p < sub > k </ sub >) is a product for the A < sub > k </ sub >

*( A < sub > 1 </ sub > ⊕ ··· ⊕ A < sub > n </ sub >, i < sub > k </ sub >) is a coproduct for the A < sub > k </ sub >.

*( That player is in ) civilians: The player is not in uniform.

*( They ) couldn't beat the Sisters of Mercy: The team is getting beat badly.

*( They ) couldn't throw a pea into the ocean: The team's shooting is really awful.

*( 1 ) Elizabeth, daughter of George Gordon, 4th Earl of Huntly and Elizabeth Keith, by whom he had two daughters, one of them Elizabeth Stewart, wife of Hugh Fraser, 5th Baron Lovat ( this union led to descent of James Monroe, 5th President of the U. S. A .), Robert Stewart, 6th Earl of Lennox and James Stewart, Earl of Arran ; and

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*( c ) It may be granted upon condition, cujus est dare, ejus est disponere, and this denization of an alien may come about three ways: by Parliament ; by letters patent, which was the usual manner ; and by conquest.

:: 1973, 1995 *( Ajax also won in 1972, however, UEFA only sanctioned the UEFA Super Cup for the first time in 1973 so the 1972 edition was an unofficial one.

*( V ) always returns the value x used in the most recent ( V, x ) operation on the same variable V.

* RF — Range factor: 9 *( putouts + assists )/ innings played.

*( 1919 ) Baruch College ( as City College ’ s School of Business and Civic Administration, renamed in 1953 to honor Bernard M. Baruch )

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In this case, we might compute T = A *( B * D ) only once and simply blend T * C to produce F, a single operation.

*( aRc ∧ bRc ) → aRb = ( aRa ∧ bRa ) → aRb erase T ∧ = bRa → aRb.

*( aRc ∧ bRc ) → aRb = ( aRc ∧ cRb ) → aRb.

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*( Thematically compiled comparison of the parallels in the ancient sources ) Dead at 2009 / 09 / 22.

*( EF2 ) For all nonzero a and b in R,.

*( 2 ) the reciprocal of the denominator less the numerator of tan A.

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*( c. 94 ) Antiquities of the Jews, or Jewish Antiquities, or Antiquities of the Jews / Jewish Archeology ( frequently abbreviated AJ, AotJ or Ant.

*( c. 97 ) Flavius Josephus Against Apion, or Against Apion, or Contra Apionem, or Against the Greeks, on the antiquity of the Jewish people ( usually abbreviated CA )

*( c. 99 ) The Life of Flavius Josephus, or Autobiography of Flavius Josephus ( abbreviated Life or Vita )

*( together with Schmeller ) Lateinische Gedichte des X. und XI.

*( 1 ) There shall be an armed forces for the Federation which shall consist of an army, a navy, an air force and such other branches of the armed forces of the Federation as may be established by an Act of the National Assembly.

*( c ) Suppress insurrection and act in aid of civil authorities to restore order when called upon to do so by the d. President but subject to such conditions as may be prescribed by an Act of the National Assembly.