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Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.

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## 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

**.**

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