If S is compact but not closed, then it has an accumulation point a not in S. Consider a collection consisting of an open neighborhood N ( x ) for each x ∈ S, chosen small enough to not intersect some neighborhood V < sub > x </ sub > of a.

Consider an open subset U of the complex plane C. Let a be an element of U, and f: U

Consider for instance the open unit disc, a non-compact Riemann surface without boundary, with curvature 0 and with Euler characteristic 1: the Gauss – Bonnet formula does not work.

Consider an open set on the real line and a function f defined on that set with real values.

Consider the open covering of which consists of:

Consider a scheme X and a cover by affine open subschemes Spec A < sub > i </ sub >.

Consider too, with what force, diligence and vivacity he has rendered back all this which in Johnson's neighbourhood, his " open sense " had so eagerly and freely taken in.

Consider the number N ( r ) of balls of radius at most r required to cover X completely.

They are maps from flat 3-space into the Lie group G. Consider now glueing these two balls together at their boundary S².

Consider an urn containing blue and yellow balls.

Consider a sphere B < sub > 2 </ sub > of radius 2 centered at N. The inversion with respect to B < sub > 2 </ sub > transforms B into its stereographic projection P.

Consider a fixed circle of radius centered at the origin.

Consider 3 bidders A, B, and C, and two homogeneous items bid upon, Y and Z.

Consider the case where " a " is assigned to a → bδ during step 1: upon membrane 3 dissolving only a single " b " and two " c " objects would exist, leading to the creation of only a single " e " object to eventually be passed out as the computation ’ s result.

Consider Quine's example of the word " gavagai " uttered by a native upon seeing a rabbit.

Consider a rectangular area a by b, and any common divisor c that divides both a and b exactly.

Consider for example a sample Java fragment to represent some common farm " animals " to a level of abstraction suitable to model simple aspects of their hunger and feeding.

Consider the following situation in a 3-boat team race ( the most common format ).

Consider a polygon P and a triangle T, with one edge in common with P. Assume Pick's theorem is true for both P and T separately ; we want to show that it is also true to the polygon PT obtained by adding T to P. Since P and T share an edge, all the boundary points along the edge in common are merged to interior points, except for the two endpoints of the edge, which are merged to boundary points.

Consider the common case of a floor in a game: the fill area is far wider than it is tall.

* Consider the development of common regional and continental policies in the agricultural sector.

Consider also the grade point average.

Geometric arrangement for Fresnel's calculation Consider the case of a point source located at a point P < sub > 0 </ sub >, vibrating at a frequency f. The disturbance may be described by a complex variable U < sub > 0 </ sub > known as the complex amplitude.

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 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.

Again we start with a C < sup >∞</ sup > manifold, M, and a point, x, in M. Consider the ideal, I, in C < sup >∞</ sup >( M ) consisting of all functions, ƒ, such that ƒ ( x ) = 0.

Consider the system at the point it has reached equilibrium.

Consider a point charge q with position ( x, y, z ).

Consider a particular bundle and take the total derivative of about this point:

Consider the class of all regular paths from a point p to another point q.

Consider as an example the interaction between a star and a distant galaxy: The error arising from combining all the stars in the distant galaxy into one point mass is negligible.

Consider the space of real-valued functions together with a special point.

We say that the number x is a periodic point of period m if f < sup > m </ sup >( x ) = x ( where f < sup > m </ sup > denotes the composition of m copies of f ) and having least period m if furthermore f < sup > k </ sup >( x ) ≠ x for all 0 < k < m. We are interested in the possible periods of periodic points of f. Consider the following ordering of the positive integers:

Consider a massless rigid rod of length l with a point mass m at one end and rotating about the other end.

Consider first one mole of gas which is composed of non-interacting point particles

Consider the point 1 ∈ R < sup >+</ sup >, and x ∈ R an element of the tangent space at 1.

Suppose S ' is in relative uniform motion to S with velocity v. Consider a point object whose position is given by r

Consider a valid line to be one where every point is within distance w / 2 of the line ( that is, lies on a track of width w, where w << d ).

Consider, for purposes of illustration, a mountainous landscape M. If f is the function sending each point to its elevation, then the inverse image of a point in ( a level set ) is simply a contour line.

Consider climbing up the connectivity ladder — assume X is a simply-connected CW-complex whose 0-skeleton consists of a point.

Consider a sphere S ( r ) with radius r. A point on the sphere is identified by its latitude φ and longitude λ, for which we introduce the random variables Φ and Λ that take values in Ω < sub > 1 </ sub > = respectively Ω < sub > 2 </ sub > =.