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Every group can be trivially made into a topological group by considering it with the discrete topology ; such groups are called discrete groups.

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## Some Related Sentences

Every and group

Group actions / representations:

__Every____group__G**can****be**considered as**a**category**with****a**single object whose morphisms**are****the**elements of G**.**A functor from G to Set is then nothing but**a**__group__action of G on**a**particular set, i**.**e**.****a**G-set**.**__Every__galaxy of sufficient mass in

**the**Local Group has an associated

__group__of globular clusters, and almost every large galaxy surveyed has been found to possess

**a**system of globular clusters

**.**

*

__Every__Lie__group__is parallelizable, and hence an orientable manifold ( there is**a**bundle isomorphism between its tangent bundle and**the**product of itself**with****the**tangent space at**the**identity )__Every__instrumental

__group__( or section ) has

**a**principal who is generally responsible for leading

**the**

__group__and playing orchestral solos

**.**

*

__Every__closed subgroup of**a**profinite__group__is itself profinite**;****the****topology**arising from**the**profiniteness agrees**with****the**subspace**topology****.**
While he admits

**the**existence of caste-based discrimination, he writes that "__Every__social__group__cannot**be**regarded as**a**race simply because we want to protect**it**against prejudice and discrimination ".__Every__summer

**the**

__group__gathers in Newport, RI for week long dance training, seaside teas, and evenings enjoying

**the**splendors of

**the**Gilded Age

**.**

*

__Every__finitely generated__group__**with****a**recursively enumerable presentation and insoluble word problem is**a**subgroup of**a**finitely presented__group__**with**insoluble word problem__Every__synset contains

**a**

__group__of synonymous words or collocations (

**a**collocation is

**a**sequence of words that go together to form

**a**specific meaning,

**such**as " car pool "); different senses of

**a**word

**are**in different synsets

**.**

__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__subgroup of

**a**

**topological**

__group__is itself

**a**

**topological**

__group__when given

**the**subspace

**topology**

**.**

__Every__ten years, when

**the**general census of population takes place, each citizen has to declare which linguistic

__group__they belong or want to

**be**aggregated to

**.**

Every and can

__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__information exchange between living organisms — i

**.**e

**.**transmission of signals that involve

**a**living sender and receiver

__can__

**be**considered

**a**form of communication

**;**and even primitive creatures

**such**as corals

**are**competent to communicate

**.**

__Every__context-sensitive grammar which does not generate

**the**empty string

__can__

**be**transformed

**into**an equivalent one in Kuroda normal form

**.**

__Every__grammar in Chomsky normal form is context-free, and conversely, every context-free grammar

__can__

**be**transformed

**into**an equivalent one which is in Chomsky normal form

**.**

__Every__module over

**a**division ring has

**a**basis

**;**linear maps between finite-dimensional modules over

**a**division ring

__can__

**be**described

**by**matrices, and

**the**Gaussian elimination algorithm remains applicable

**.**

__Every__entire function

__can__

**be**represented as

**a**power series that converges uniformly on compact sets

**.**

__Every__sequence

__can__, thus,

**be**read in three reading frames, each of which will produce

**a**different amino acid sequence ( in

**the**given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).

__Every__hyperbola is congruent to

**the**origin-centered East-West opening hyperbola sharing its same eccentricity ε ( its shape, or degree of " spread "), and is also congruent to

**the**origin-centered North-South opening hyperbola

**with**identical eccentricity ε — that is,

**it**

__can__

**be**rotated so that

**it**opens in

**the**desired direction and

__can__

**be**translated ( rigidly moved in

**the**plane ) so that

**it**is centered at

**the**origin

**.**

__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__species

__can__

**be**given

**a**unique ( and, one hopes, stable ) name, as compared

**with**common names that

**are**often neither unique nor consistent from place to place and language to language

**.**

__Every__vector v in determines

**a**linear map from R to taking 1 to v, which

__can__

**be**thought of as

**a**Lie algebra homomorphism

**.**

__Every__use of modus tollens

__can__

**be**converted to

**a**use of modus ponens and one use of transposition to

**the**premise which is

**a**material implication

**.**

__Every__adult, healthy, sane Muslim who has

**the**financial and physical capacity to travel to Mecca and

__can__make arrangements for

**the**care of his / her dependants during

**the**trip, must perform

**the**Hajj once in

**a**lifetime

**.**

*

__Every__finite**topological**space gives rise to**a**preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder__can__**be**formed as**the**specialization preorder of**a****topological**space in this way**.**
*

__Every__preorder__can__**be**given**a****topology**,**the**Alexandrov**topology****;**and indeed, every preorder on**a**set is in one-to-one correspondence**with**an Alexandrov**topology**on that set**.**__Every__binary relation R on

**a**set S

__can__

**be**extended to

**a**preorder on S

**by**taking

**the**transitive closure and reflexive closure, R < sup >+=</ sup >.

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