 Page "Pointless topology" ¶ 2
from Wikipedia ## Some Related Sentences

Formally and frame Formally, this effect is referred to as and is a process whereby the capture frame rate of the camera changes over time. Formally, a frame on a homogeneous space G / H consists of a point in the tautological bundle G → G / H.

Formally and is Formally organized vocational programs supported by federal funds allow high school students to gain experience in a field of work which is likely to lead to a full-time job on graduation. Formally, a binary operation on a set S is called associative if it satisfies the associative law: Formally, their designation is the letter Ž and the number. Formally, a topological space X is called compact if each of its open covers has a finite subcover. Formally, the set of all context-free languages is identical to the set of languages accepted by pushdown automata ( PDA ). Formally, the derivative of the function f at a is the limit More rigorously, the divergence of a vector field F at a point p is defined as the limit of the net flow of F across the smooth boundary of a three dimensional region V divided by the volume of V as V shrinks to p. Formally, Formally, the base is known as Naval Support Facility Diego Garcia ( the US activity ) or Permanent Joint Operating Base ( PJOB ) Diego Garcia ( the UK's term ). Formally, there is a clear distinction: " DFT " refers to a mathematical transformation or function, regardless of how it is computed, whereas " FFT " refers to a specific family of algorithms for computing DFTs. Formally, oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100 % ionic. Formally, a bifunctor is a functor whose domain is a product category. Formally, a set S is called finite if there exists a bijection Formally, the system is said to have memory. Formally, an inner product space is a vector space V over the field together with an inner product, i. e., with a map Formally, if M is a set, the identity function f on M is defined to be that function with domain and codomain M which satisfies * Formally, when working over the reals, as here, this is accomplished by considering the limit as ε → 0 ; but the " infinitesimal " language generalizes directly to Lie groups over general rings. Formally, a profinite group is a Hausdorff, compact, and totally disconnected topological group: that is, a topological group that is also a Stone space. Formally, this sharing of dynamics is referred to as universality, and systems with precisely the same critical exponents are said to belong to the same universality class. Formally, Φ = kx − ωt is the phase.

Formally and defined Formally, as per the 2002 Memorandum of Understanding between the BSI and the United Kingdom Government, British Standards are defined as: Formally speaking, a collation method typically defines a total order on a set of possible identifiers, called sort keys, which consequently produces a total preorder on the set of items of information ( items with the same identifier are not placed in any defined order ). Formally, these reside in a complex separable Hilbert space-variously called the " state space " or the " associated Hilbert space " of the system-that is well defined up to a complex number of norm 1 ( the phase factor ). Formally it is defined by the equation Limits and colimits in a category C are defined by means of diagrams in C. Formally, a diagram of type J in C is a functor from J to C: Formally, the convex hull may be defined as the intersection of all convex sets containing X or as the set of all convex combinations of points in X. Formally, a unique factorization domain is defined to be an integral domain R in which every non-zero and non-unit x of R can be written as a product ( including an empty product ) of irreducible elements p < sub > i </ sub > of R and a unit u: Formally, a transductive support vector machine is defined by the following primal optimization problem: Formally, powers with positive integer exponents may be defined by the initial condition Formally, bending modulus is defined as the energy required to deform a membrane from its intrinsic curvature to some other curvature. Formally, a Menger sponge can be defined as follows: Formally, a constraint satisfaction problem is defined as a triple, where is a set of variables, is a domain of values, and is a set of constraints. Formally, the case where only a subset of parameters is defined is still a composite hypothesis ; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic ( the distribution under the null hypothesis ) does not depend on the parameters whose values have not been specified under the point null hypothesis. Formally, the index of H in G is defined as the number of cosets of H in G. ( The number of left cosets of H in G is always equal to the number of right cosets. Formally, the subhypergraph induced by a subset of is defined as Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces. Formally, a cardinal κ is defined to be weakly compact if it is uncountable and for every function f: < sup > 2 </ sup > → Formally, a Coxeter group can be defined as a group with the presentation Formally, the Cantor function c: → is defined as follows: Formally, the sets of free and bound names of a process in π – calculus are defined inductively as follows. Formally, the mutual information of two discrete random variables X and Y can be defined as: Formally, an absolute coequalizer of a pair in a category C is a coequalizer as defined above but with the added property that given any functor F ( Q ) together with F ( q ) is the coequalizer of F ( f ) and F ( g ) in the category D. Split coequalizers are examples of absolute coequalizers.

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