[permalink] [id link]

Every continuous function on a compact set is uniformly continuous.

from
Wikipedia

## Some Related Sentences

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__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__

__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__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__

__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

**.**

Every and function

__Every__such subset has

**a**smallest element, so to specify our choice

__function__we can simply say that it maps each

**set**to the least element of that

**set**

**.**

__Every__effectively calculable

__function__( effectively decidable predicate )

**is**general recursive italics

__Every__bijective

__function__g has an inverse g < sup >− 1 </ sup >, such that gg < sup >− 1 </ sup > = I ;

__Every__entire

__function__can be represented as

**a**power series that converges

**uniformly**

**on**

**compact**sets

**.**

__Every__holomorphic

__function__can be separated into its real and imaginary parts, and each of these

**is**

**a**solution of Laplace's equation

**on**R < sup > 2 </ sup >.

__Every__completely multiplicative

__function__

**is**

**a**homomorphism of monoids and

**is**completely determined by its restriction to the prime numbers

**.**

__Every__time another object or customer enters the line to wait, they join the end of the line and represent the “ enqueue ”

__function__

**.**

__Every__type that

**is**

**a**member of the type class defines

**a**

__function__that will extract the data from the string representation of the dumped data

**.**

__Every__output of an encoder can be described by its own transfer

__function__, which

**is**closely related to the generator polynomial

**.**

Every and on

__Every__day, when the President took his nap, Rob Roy would stretch out

__on__the window seat near him, like

**a**perfect gentleman, and stare thoughtfully out the window, or he would take

**a**little nap himself

**.**

__Every__man who dabbles in the market to make

**a**little easy money

__on__the side and suffers losses could at the time hardly face his wife who was wondering how her husband could be so dumb

**.**

__Every__few minutes she would awaken for

**a**moment to review things: Stowey, yes, was

__on__his way south, and the two boys were away in school, and nothing was burning

__on__the stove, and Lucretia was coming for dinner and bringing three guests of hers

**.**

__Every__night they all went to Mama and Papa Albright's, and sat

__on__the open front porch, where they could get the breeze

**.**

__Every__few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely

__on__the Rotunda pavement, supported as it

**is**by ancient brick vaulting

**.**

__Every__night when he wanted

**a**drink of water, didn't he practice being fearless by not turning

__on__the bathroom light??

__Every__single instance of altruistic behavior need not always increase inclusive fitness ; altruistic behaviors would have been selected for if such behaviors

__on__average increased inclusive fitness in the ancestral environment

**.**

__Every__year,

__on__the last Sunday in April, there

**is**an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth

**.**

__Every__actor who has opened in the role of Pseudolus

__on__Broadway ( Zero Mostel, Phil Silvers and Nathan Lane ) won

**a**Best Actor Tony Award for their performance

**.**

* Revised Code of Washington 9

**.**12**.**010: "__Every__person who brings__on__his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass**a**defendant in the suit, or who serves or sends any paper or document purporting to be or resembling**a**judicial process, that**is**not in fact**a**judicial process,**is**guilty of**a**misdemeanor ; and in case the person offending**is**an attorney, he or she may, in addition thereto be disbarred from practicing law within this state**.**__Every__year, the European Joint Conferences

__on__Theory and Practice of Software ( ETAPS ) sponsors the International Conference

__on__Compiler Construction ( CC ), with papers from both the academic and industrial sectors

**.**

__Every__Halloween, Dabney House conducts the infamous " Millikan pumpkin-drop experiment " from the top of Millikan Library, the highest point

__on__campus

**.**

__Every__person should be identified uniquely as resident in one place but where they happen to be

__on__census day, their de facto residence, may not be the best place to count them

**.**

0.115 seconds.