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Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.
Some Related Sentences
Every and special
Every bullet diameter, and most of the bullet types, need special dies, making swaging a rather investition-intensive enterprise.
Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.
The philosophe Condillac observed in 1782 that " Every science requires a special language because every science has its own ideas.
Every three months, it publishes a " Technology Quarterly ," a special section focusing on recent trends and developments in science and technology.
Every year, the post office also creates a special Christmas hand-cancellation pictorial postmark for use during December, which also attracts mail from all over the world.
* Every year in November, the Friday after Thanksgiving marks the start of Coeur d ' Alene's Christmas Lighting Ceremony including a parade, fireworks and special holiday candles given out by the local downtown businesses.
Every two weeks, the prisoners receive “ a special meal of pork broth soup and white-flour steamed buns .” Important Chinese holidays such as New Year ’ s, National Day, and the Spring Festival are celebrated with meat dumplings, a special treat in an otherwise meatless diet.
§ 1: " Every subject expects from the territorial prince security and protection, so it is the duty of the territorial prince, the rights of subjects to determine clearly and to guide the way of the actions how it is needed by universal and special prosperity.
Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.
Every year the municipality hosts a special festival remembering the days when local people emigrated to the new world.
The New York Times reports, " Every month, hundreds of South Korean men fly to Vietnam, the Philippines, Mongolia, Nepal and Uzbekistan on special trips ".
Every H * is very special in structure: it is pure-injective ( also called algebraically compact ), which says more or less that solving equations in H * is relatively straightforward.
Every province has a Communist Party of China provincial committee, headed by a secretary beside the two special administrative regions.
Every other borough in Connecticut is a special services district located within another town, the unit of Connecticut local government.
Every year a new Feluda adventure appeared in the special Autumn edition or Durgapuja edition of the Bengali periodical-Desh, and also in Sandesh.
Every governor since Ronald Reagan in 1968 has been subject to a recall effort, but Gray Davis was the first governor whose opponents gathered the necessary signatures to qualify for a special election.
This is really a special case of a more general fact: Every continuous function from a compact space into a metric space is bounded.
Every civilization starts with certain special abilities, specifically two traits that give them bonuses that help in corresponding areas of gameplay ; they also determine what two technologies the civilization begins the game with.
Every woman on becoming a member of the Society chooses one of the girls in the orphanage and makes her the object of her special care and solicitude.
Every vector space is free, and the free vector space on a set is a special case of a free module on a set.
Every territorial force has a specialist Firearms Unit, which maintains Armed Response Vehicles to respond to firearms related emergency calls, while one territorial force ( the Police Service of Northern Ireland ) and two of the special police forces, ( the Civil Nuclear Constabulary and the Ministry of Defence Police ) are routinely armed.
Every year 11th lunar month a series of special mystical practices are performed in the upper house for a week.
Every blister that contains a Wizard includes a free Incantation Rules Booklet as well as cards that describe magic items and special spells particular to each.
Every and uniformly
Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).
Every entire function can be represented as a power series that converges uniformly on compact sets.
Every topological group can be viewed as a uniform space in two ways ; the left uniformity turns all left multiplications into uniformly continuous maps while the right uniformity turns all right multiplications into uniformly continuous maps.
Every experiment in such a free-falling environment has the same results as it would for an observer at rest or moving uniformly in deep space, far from all sources of gravity.
Every and continuous
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.
* Every compact Hausdorff space of weight at most ( see Aleph number ) is the continuous image of ( this does not need the continuum hypothesis, but is less interesting in its absence ).
Every place south of the Antarctic Circle experiences a period of twenty-four hours ' continuous daylight at least once per year, and a period of twenty-four hours ' continuous night time at least once per year.