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* Every totally bounded metric space is bounded.
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Every and totally
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.
Every November the Reebok Stadium hosts Kidz up North which is one of the largest free UK exhibitions totally dedicated to children with disabilities and special needs, their parents, carers and professionals who work with them.
Every subset of a totally bounded space is a totally bounded set ; but even if a space is not totally bounded, some of its subsets still will be.
Every and bounded
* Every separable metric space is isometric to a subset of the ( non-separable ) Banach space l < sup >∞</ sup > of all bounded real sequences with the supremum norm ; this is known as the Fréchet embedding.
Every finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.
This is really a special case of a more general fact: Every continuous function from a compact space into a metric space is bounded.
For example, to study the theorem “ Every bounded sequence of real numbers has a supremum ” it is necessary to use a base system which can speak of real numbers and sequences of real numbers.
Every maximal outerplanar graph with n vertices has exactly 2n − 3 edges, and every bounded face of a maximal outerplanar graph is a triangle.
Every three years the Company makes an award to the three buildings or structures, in the area bounded by the M25 motorway, which respectively embody the most outstanding example of brickwork, of slated or tiled roof and of hard-surface tiled wall and / or floor.
Every Polish town was bounded to put up a quantity of soldiers-this was a conspicuous sign of a power of a given town how much soldiers it had to put up.
Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.
Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to.
Every bounded positive-definite measure μ on G satisfies μ ( 1 ) ≥ 0. improved this criterion by showing that it is sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ < sup >– ½ </ sup > f has non-negative integral with respect to Haar measure, where Δ denotes the modular function.
Every topological vector space X gives a bornology on X by defining a subset to be bounded iff for all open sets containing zero there exists a with.
Every ( bounded ) convex polytope is the image of a simplex, as every point is a convex combination of the ( finitely many ) vertices.
Every and metric
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every smooth submanifold of R < sup > n </ sup > has an induced Riemannian metric g: the inner product on each tangent space is the restriction of the inner product on R < sup > n </ sup >.
Every building has a canonical length metric inherited from the geometric realisation obtained by identifying the vertices with an orthonormal basis of a Hilbert space.
# Every Riemannian metric on a Riemann surface is Kähler, since the condition for ω to be closed is trivial in 2 ( real ) dimensions.
Every hyperkähler manifold M has a 2-sphere of complex structures ( i. e. integrable almost complex structures ) with respect to which the metric is Kähler.
Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.
Every metric space which is ccc is also separable, but in general a ccc topological space need not be separable.
Every locally compact group which is second-countable is metrizable as a topological group ( i. e. can be given a left-invariant metric compatible with the topology ) and complete.
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