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Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.

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## Some Related Sentences

Any and subset

__Any__one language has only a

__subset__

**of**the aspectual distinctions attested in the world's languages, and some languages

**(**such as Standard German ; see below

**)**do not have aspects

**.**

__Any__topological space which

**is**

**itself**finite or countably infinite

**is**separable, for the whole space

**is**a countable dense

__subset__

**of**

**itself**

**.**

__Any__second-countable space

**is**separable: if

**is**a countable base, choosing any gives a countable dense

__subset__

**.**

__Any__

__subset__

**of**resource, but typically at least the processor state, may be associated

**with**each

**of**the process ' threads in operating systems

**that**support threads or ' daughter ' processes

**.**

*

__Any__**open**__subset__**of**a finite-dimensional real, and therefore complex, vector space**is**a diffeological space**.**__Any__discrete

__subset__

**of**Euclidean space

**is**countable, since the isolation

**of**each

**of**

**its**points

**(**together

**with**the fact the rationals are dense in the reals

**)**means

**that**it may be mapped 1-1

**to**a set

**of**points

**with**rational co-ordinates,

**of**which there are only countably many

**.**

__Any__proposed inverse

**R**

**of**F

**(**reconstruction formula, in the lingo

**)**would have

**to**map

**to**some

__subset__

**of**

**.**

__Any__action

**of**the group by continuous affine transformations on a compact convex

__subset__

**of**a

**(**separable

**)**locally convex topological vector space has a fixed point

**.**

__Any__induced subgraph

**of**a comparability graph

**is**

**itself**a comparability graph, formed from the restriction

**of**the partial order

**to**a

__subset__

**of**

**its**elements

**.**

*

__Any__directed set A may be made into a Cauchy space by declaring a filter F**to**be Cauchy if, given any element**n****of**A, there**is**an element U**of**F such**that**U**is**either a singleton or a__subset__**of**the tail__Any__set

**of**five points in the plane in general position has a

__subset__

**of**four points

**that**form the vertices

**of**a convex quadrilateral

**.**

Any and R

*

__Any__ring**of**matrices**with**coefficients in a commutative ring__R__forms an R-algebra under matrix addition and multiplication**.**
Brown continued releasing recordings: in 1993, he issued the album, Universal James, which included Brown's final Billboard charted single, " Can't Get

__Any__Harder ", which peaked at # 76 on the US__R__& B chart and # 59 on the UK chart**.**__Any__formal series

**with**has a composition inverse provided

**is**an invertible element

**of**

__R__

**.**The coefficients are found recursively from the above formula for the coefficients

**of**a composition, equating them

**with**those

**of**the composition identity X

**(**

**that**

**is**1 at degree 1 and 0 at every degree greater than 1

**)**

**.**

*

__Any__positive multiple**of**the repunit__R__**<**sub**>****n****</**sub ><**sup**>( b )</**sup****>**contains at least**n**nonzero digits in base b**.**__Any__binary relation

__R__on a set A can generate a natural partial order on the R-cycle equivalence classes

**of**set A, so

**that**xRy implies ≥

**.**

* The Drug War in Mexico: By

__Any__Other Name it's Terrorism, by Barnard__R__**.**Thompson**(**MexiData**.**info**)**__Any__totally ordered set

**that**

**is**not isomorphic

**to**

__R__but satisfies

**(**1

**)**–

**(**4

**)**

**is**known as a Suslin line

**.**

__Any__physical object whose radius

__R__becomes less than or equal

**to**the Schwarzschild radius will undergo gravitational collapse and become a black hole

**.**

*

__Any__ring__R__can be considered as a one-object preadditive category ; the category**of**left modules over__R__**is**the same as the additive functor category Add**(**__R__, Ab**)****(**where Ab denotes the category**of**abelian groups ), and the category**of**right R-modules**is**Add**(**__R__**<****sup****>**op**</****sup**>, Ab ).__Any__n-dimensional formal group law gives an

**n**dimensional Lie algebra over the ring

__R__, defined in terms

**of**the quadratic part F

**<**sub

**>**2

**</**sub

**>**

**of**the formal group law

**.**

*

__Any__slave who evades capture for 20 days or more**is****to**be publicly whipped for the first offense ; branded**with**the letter__R__on the right cheek for the second offense ; and lose one ear if absent for thirty days for the third offense ; and castrated for the fourth offense**.**
In early June, Banks released the second single off the album, "

__Any__Girl " featuring__R__& B singer Lloyd**.**
O

**.**A**.**__R__., who grew up in nearby Rockville, Maryland, recorded the live album__Any__Time Now at the 9: 30 Club on November 23 – 24, 2001**.**__Any__non-singular matrix S

**of**the same size

**is**said

**to**transform A into

**another**symmetric matrix B = SAS

**<**

**sup**

**>**T

**</**

**sup**>, also

**of**order

**n**, where S

**<**

**sup**

**>**T

**</**

**sup**

**>**

**is**the transpose

**of**S

**.**If A

**is**the coefficient matrix

**of**some quadratic form

**of**

__R__

**<**

**sup**

**>**

**n**

**</**

**sup**>, then B

**is**the matrix for the same form after the change

**of**coordinates defined by S

**.**

Lloyd C

**.**Gardner, " Pay__Any__Price: Lyndon Johnson and the Wars for Vietnam ", Chicago: Ivan__R__**.**Dee, 1995**.**

Any and <

Note:

__Any__nonlinear electronic block driven by two signals**with**frequencies f__<__sub**>**1**</**sub**>**and f__<__sub**>**2**</**sub**>**would generate intermodulation**(**mixing**)**products**.**__Any__units

**of**angular measure can be used for right ascension, but it

**is**customarily measured in hours (<

**sup**

**>**h

**</**

**sup**>), minutes (<

**sup**

**>**m

**</**

**sup**>), and seconds (<

**sup**

**>**s

**</**

**sup**>),

**with**24

__<__

**sup**

**>**h

**</**

**sup**

**>**being equivalent

**to**a full circle

**.**

__Any__frequency component above f

__<__sub

**>**s

**</**sub >/ 2

**is**indistinguishable from a lower-frequency component, called an alias, associated

**with**one

**of**the copies

**.**

#

__Any__pure element**(**even if it forms diatomic molecules like chlorine, Cl__<__sub**>**2**</**sub >) has an oxidation state**(**OS**)****of**zero**.**__Any__Taylor series for this function converges not only for x close enough

**to**x

__<__sub

**>**0

**</**sub

**>**

**(**as in the definition

**)**but for all values

**of**x

**(**real or complex ).

__Any__polynomial written in standard form has a unique constant term, which can be considered a coefficient

**of**x

__<__

**sup**

**>**0

**</**

**sup**>.

__<__li

**>**

__Any__legislative measures and other measures calculated

**to**prevent a racial group or groups from participation in the political, social, economic and cultural life

**of**the country and the deliberate creation

**of**conditions preventing the full development

**of**such a group or groups, in particular by denying

**to**members

**of**a racial group or groups basic human rights and freedoms, including the right

**to**work, the right

**to**form recognised trade unions, the right

**to**education, the right

**to**leave and

**to**return

**to**their country, the right

**to**a nationality, the right

**to**freedom

**of**movement and residence, the right

**to**freedom

**of**opinion and expression, and the right

**to**freedom

**of**peaceful assembly and association ;</ li

**>**

__<__li

**>**

__Any__measures including legislative measures, designed

**to**divide the population along racial lines by the creation

**of**separate reserves and ghettos for the members

**of**a racial group or groups, the prohibition

**of**mixed marriages among members

**of**various racial groups, the expropriation

**of**landed property belonging

**to**a racial group or groups or

**to**members thereof ;</ li

**>**

__Any__XML Schema can use the Point Profile by importing it and referencing the subject

__<__gml: Point

**>**instance:

__Any__number b + 1

**is**written as " 11

__<__sub

**>**b

**</**sub >" in base b, so 11

**is**trivially a palindrome in base 10

**.**

__Any__such sequence belongs

**to**the Hilbert space ℓ

__<__sub

**>**2

**</**sub >, so the Hilbert cube inherits a metric from there

**.**

:: Theorem

**(**Lefschetz theorem on**(**1, 1 )- classes**)**__Any__element**of**H__<__**sup****>**2**</****sup**>( X, Z**)**∩ H__<__**sup****>**1, 1**</****sup**>( X**)****is**the cohomology class**of**a divisor on X**.**__Any__

**n**×

**n**real symmetric matrix A determines a quadratic form q

__<__sub

**>**A

**</**sub

**>**in

**n**variables by the formula

__Any__sulfur in the fuel can be oxidized

**to**SO

__<__sub

**>**2

**</**sub

**>**

**(**sulfur dioxide

**)**or even SO

__<__sub

**>**3

**</**sub

**>**

**(**sulfur trioxide

**)**in the combustion chamber

**.**

__Any__non-zero vector v divides the Euclidean space into two half-spaces bounding the hyperplane v

__<__

**sup**>∧</

**sup**

**>**orthogonal

**to**v, namely v

__<__

**sup**>+</

**sup**

**>**and v

__<__

**sup**>−</

**sup**>.

0.738 seconds.