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Consider a topological space, that is, a space with some notion of closeness between points in the space.
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Consider and topological
Fundamental group: Consider the category of pointed topological spaces, i. e. topological spaces with distinguished points.
Consider a function from a metric space M to a topological space V, and a point c of M. We direct the set M
Consider first the set of all possible singular n-simplices on a topological space X.
Consider first that is a map from topological spaces to free abelian groups.
Consider any topological space X.
Consider the cartesian product of topological spaces, indexed by some index.
Consider and space
Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.
Consider two observers O and O ', each using their own Cartesian coordinate system to measure space and time intervals.
Consider as above systems and each with a Hilbert space,.
Consider a closed loop of string, left to move through space without external forces.
Consider these three things we say about God: first, God is a spirit ; second, God is the creator of the world ; and third, God exists apart from space and time.
Consider a space ship traveling from Earth to the nearest star system outside of our solar system: a distance years away, at a speed ( i. e., 80 percent of the speed of light ).
Consider, for example, the difference between strong and weak convergence of functions in the Hilbert space L < sup > 2 </ sup >( R < sup > n </ sup >).
Consider a domain D in m-dimensional x space, with boundary B.
Consider a sample space generated by two random variables and.
Consider Phlebas, first published in 1987, is a space opera novel by Scottish writer Iain M. Banks.
Consider a loop accessing locations in an equidistant pattern, i. e. the path in the spatial-temporal coordinate space is a dotted line.
Consider the space of real-valued functions together with a special point.
Consider the polynomial ring R, and the irreducible polynomial The quotient space is given by the congruence As a result, the elements ( or equivalence classes ) of are of the form where a and b belong to R. To see this, note that since it follows that,,, etc.
Consider the complex Hilbert space L < sup > 2 </ sup > and the differential operator
Consider the complex Hilbert space L < sup > 2 </ sup >( R ), and the operator which multiplies a given function by x:
Consider the space for a maze being a large grid of cells ( like a large chess board ), each cell starting with four walls.
Consider for instance the Banach space l < sup >∞</ sup > of all bounded real sequences.
Consider in a vector space V, the general linear group GL ( V ).
Consider the point 1 ∈ R < sup >+</ sup >, and x ∈ R an element of the tangent space at 1.
Consider an-dimensional space, foliated as a product by subspaces consisting of points whose first co-ordinates are constant.
Consider the first-order differential operators D < sub > i </ sub > to be infinitesimal operators on Euclidean space.
Consider a smooth surface S in 3-dimensional Euclidean space R < sup > 3 </ sup >.
Consider and is
Consider what you have to earn to be able to spend the $3,000 and your building time is well worth it.
Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.
Consider a simple, closed, plane curve C which is a real-analytic image of the unit circle, and which is given by Af.
Here is an everyday experience of the basic nature of the Descartes experiment: Consider sitting in your train and noticing a train originally at rest beside you in the railway station pulling away.
Consider the subset sum problem, an example of a problem that is easy to verify, but whose answer may be difficult to compute.
( Consider 1 / 0, which is defined with the value of infinity, vs. 0 / 0, which is undefined.
Consider a car's cruise control, which is a device designed to maintain vehicle speed at a constant desired or reference speed provided by the driver.
* Consider the modulo 2 equivalence relation on the set of integers: if and only if their difference is an even number.
Consider the following sentences: " Socrates is a philosopher ", " Plato is a philosopher ".
* Consider now L = Q ( ³ √ 2, ω ), where ω is a primitive third root of unity.
Consider a pseudo random number generator ( PRNG ) function P ( key ) that is uniform on the interval 2 < sup > b </ sup > − 1.
Consider the context of evaluating each one of a class of events A < sub > 1 </ sub >, A < sub > 2 </ sub >, A < sub > 3 </ sub >,..., A < sub > n </ sub > ( for example, is the occurrence of the event harmful or not ?).
Consider the case in which liquid crystal molecules are aligned parallel to the surface and an electric field is applied perpendicular to the cell as in the following diagram.
Consider a binary electrolyte AB which dissociates into A + and B-ions and the equilibrium state is represented by the equation:
Consider the closed intervals for all integers k ; there are countably many such intervals, each has measure 1, and their union is the entire real line.
Consider a point, P, such that light that is initially travelling parallel to the axis of symmetry is reflected from P along a line that is perpendicular to the axis of symmetry.
Consider some set P and a binary relation ≤ on P. Then ≤ is a preorder, or quasiorder, if it is reflexive and transitive, i. e., for all a, b and c in P, we have that:
Consider an audio DSP example: if a process requires 2. 01 seconds to analyze, synthesize, or process 2. 00 seconds of sound, it is not real-time.
Consider a pointer that in a given interval of the execution is updated several times.
0.390 seconds.