Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

* Any topologically closed subgroup of a Lie group is a Lie group.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any closed interval b of real numbers is Lebesgue measurable, and its Lebesgue measure is the length b − a.

Any force that passes the closed path test for all possible closed paths is classified as a conservative force.

Any intersection of closed sets is closed ( including intersections of infinitely many closed sets ), and any union of finitely many closed sets is closed.

Eric Raymond extends this principle in support of open source security software, saying, " Any security software design that doesn't assume the enemy possesses the source code is already untrustworthy ; therefore, never trust closed source.

Any collection of subsets of a set X satisfying these properties forms a base for the closed sets of a topology on X.

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

Any of these will result in some power to the solenoid, but not enough to hold the heavy contacts closed, so the starter motor itself never spins, and the engine does not start.

" Robinson also returned to the stage in 1993 with a Broadway production of Frank Gilroy's Any Given Day, but the play closed after only six weeks.

Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions.

Any small perturbation from the closed trajectory would cause the system to return to the limit cycle, making the system stick to the limit cycle.

Any compact orientable surface and any compact surface with non-empty boundary embeds in though any closed non-orientable surface needs.

Any loose thread can be cut off with scissors or tied together to form a closed circle.

Any closed 3-manifold is the boundary of a 4-manifold.

Any finite graph has a finite ( though perhaps exponential ) number of distinct simple cycles, and if the graph is embedded into three-dimensional space then each of these cycles forms a simple closed curve.

Any young player who has good control will become a successful curve pitcher long before the pitcher who is endeavoring to master both curves and control at the same time.

Any market structure characterized by a downward sloping demand curve has market power – monopoly, monopolistic competition and oligopoly.

Any point on the frontier curve is Pareto efficient.

Any curve on the sphere that does not intersect either pole, except possibly at the endpoints, can be parametrized by

Any non-singular curve on a smooth surface will have its tangent vector T lying in the tangent plane of the surface orthogonal

Any elliptic curve in Edwards form has a point of order 4.

Any timelike curve admits a comoving observer whose " time axis " corresponds to that curve, and, since no observer is privileged, we can always find a local coordinate system in which lightcones are inclined at 45 degrees to the time axis.

Any continuous curve connecting the origin z

Any conic section defined over F with a rational point in F is a rational curve.

Any such change would have no effect on the shape of the SRVC curve and therefore its slope at any point-MC.

Any continuous deformation of the curve above is also considered a trefoil knot.

Any velocity can be interpreted as the slope of a curve ; in geometric units, slopes are evidently dimensionless ratios.

Any regular curve may be parametrized by the arc length ( the natural parametrization ) and from the point of view of a bug on the curve that does not know anything about the ambient space, all curves would appear the same.

Any time we choose a point that is rejected, we tighten the envelope with another line segment that is tangent to the curve at the point with the same x-coordinate as the chosen point.

Any deviations from a smooth curve will cause the airflow over the leeward side of the sail to separate causing a reduction in lift and reduced performance.

Any Walrasian equilibrium lies on the contract curve.

Any such surface is the Kummer variety of the Jacobian of a smooth hyperelliptic curve of genus 2 ; i. e. a quotient of the Jacobian by the Kummer involution x ↦ − x.

Any curve on a del Pezzo surface has self intersection number at least − 1.

Any curve on a weak del Pezzo surface has self intersection number at least − 2.

Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.

Any player is usually allowed to control or bet in as many boxes as desired at a single table, but it is prohibited for an individual to play on more than one table at a time or to place multiple bets within a single box.

: Premise: Any cognitive state occurs as part of a set of cognitive states and within a cognitive system

Any economist will consider the immediate opportunity cost of the logrolling procedure within the legislative body, as well as the external cost of the vote ( the cost to enact and see the bill through to fruition ).

Any individual workflow within a system of workflows can be subject to some type of operational latency.

Eugene Odum, a founder of ecology, stated: " Any unit that includes all of the organisms ( ie: the " community ") in a given area interacting with the physical environment so that a flow of energy leads to clearly defined trophic structure, biotic diversity, and material cycles ( i. e.: exchange of materials between living and nonliving parts ) within the system is an ecosystem.

Any legal wrestler is open to attack from any direction at any time, including when they are downed, as long as they are within the ring area enclosed by the ring ropes.

Any modulated signal will have an infinite number of sidebands and hence an infinite bandwidth but in practice all significant sideband energy ( 98 % or more ) is concentrated within the bandwidth defined by Carson's rule.

# Any call for which an additional charge, i. e., toll charge, is not billed to the calling or called party, or ( depending on the country ) for which this charge is reduced because it is a short-distance call ( e. g. within a town or local metropolitan area ).

Any cash flow within 12 months will not be discounted for NPV purpose.

Any amount of the donation remaining after the first year could be carried forward for fifteen additional years ( allowing a maximum of sixteen years within which the deduction may be utilized ), or until the amount of the deduction has been used up, whichever comes first.

Any code which deals with NGSCB functions must be located within the NCA.

Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.

Any children born within the wedlock or within 12 months after divorce receive the ( ex )- husband's last name, even if he is not the biological father.

Any and all feudal duchies that made up the patchwork of England have since been absorbed within the Royal Family.

: Any magistrate, or in the absence of any magistrate any commissioned officer in Her Majesty's Naval, Military or Air Force Service or any police officer above the rank of inspector, in whose view a riot is being committed, or who apprehends that a riot is about to be committed by persons being assembled within his view, may make or cause to be made a proclamation in the Queen's name, in such form as he thinks fit, commanding the rioters or persons so assembled to disperse peaceably.

Any person who does not disperse within one hour of the proclamation being read is liable to receive a maximum penalty of five years imprisonment.

Any remaining eddy currents must flow within the cross section of each individual lamination, which reduces losses greatly.

Any development would be within the London Borough of Bromley, but affect residents in neighbouring boroughs and the access to the NSC.

A higher twist than needed can also cause more subtle problems with accuracy: Any inconsistency within the bullet, such as a void that causes an unequal distribution of mass, may be magnified by the spin.

Any such structure imposes some precedent ideas of the subject matter, since ' existing discourses ' are being imported and can continue within the conference, e. g. two people who agree on a matter strongly can all attend the same sub-circles and continue to back each other up, reducing the chance that either of them will learn anything, or that anyone can learn anything from them.

Any such magistrate was also escorted by lictor bearing the fasces ( traditional symbols of imperium and authority ); when outside the pomerium, axes were added to the fasces to indicate an imperial magistrate's power to enact capital punishment outside Rome ( the axes were removed within the pomerium ).

Any one Joker card used within a meld must be identified as one card of appropriate rank and suit.