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Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.

from
Wikipedia

## Some Related Sentences

Any and point

*

__Any__locally compact Hausdorff**space**can be turned into**a**compact**space****by**adding**a**single__point__**to****it****,****by**means**of**Alexandroff one-point compactification**.**__Any__piece

**of**DNA with

**the**

__point__centromere DNA sequence on

**it**will typically form

**a**centomere if present in

**the**appropriate species

**.**

__Any__delusion on this

__point__leads

**to**

**the**greatest errors

**,**misfortunes

**,**and troubles

**,**and

**to**

**the**slavery

**of**

**the**soul

**.**

__Any__increase

**of**

**the**drain-to-source voltage will increase

**the**distance

**from**drain

**to**

**the**pinch-off

__point__

**,**increasing resistance due

**to**

**the**depletion region proportionally

**to**

**the**applied drain-to-source voltage

**.**

__Any__overbid or underbid loses

**the**number

**of**

**points**their bid was off

**(**

**a**player bidding 3 tricks

**that**wins only 2 would lose

**a**

__point__

**,**as would

**a**player bidding 2 and winning 3 ).

__Any__given procedure might be called at

**any**

__point__during

**a**program's execution

**,**including

**by**other procedures or itself

**.**

__Any__symmetry group whose elements have

**a**common fixed

__point__

**,**

**which**is true for

**all**finite symmetry groups and also for

**the**symmetry groups

**of**bounded figures

**,**can be represented as

**a**subgroup

**of**orthogonal group O

**(**n

**)**

**by**choosing

**the**origin

**to**be

**a**fixed

__point__

**.**

#

__Any__neighbourhood N**of****x**contains**a**neighbourhood M**of****x**such**that**N is**a**neighbourhood**of**each__point__**of**M**.**__Any__military planner would know

**that**

**to**mount

**a**massive invasion

**of**Europe

**from**England

**,**Allied units had

**to**be staged around

**the**country

**,**with those

**that**would land first nearest

**to**

**the**invasion

__point__

**.**

__Any__substance can be placed on

**a**section

**of**

**the**strip revealing its thermal behaviour at

**the**temperature at

**that**

__point__

**.**

__Any__object radiating sound

**,**including

**a**loudspeaker system

**,**can be thought

**of**as being composed

**of**combinations

**of**such simple

__point__sources

**.**

__Any__planetary sized body at Earth's

__point__should have been visible

**by**

**the**NASA STEREO coronagraphs during

**the**first half

**of**2007

**.**

__Any__player

**(**or

**,**in some variations

**,**only

**the**dealer

**)**may at

**any**time announce

**"**

__point__

**of**order ,"

**(**could also be

**"**Court

**of**Law

**"**or

**"**Point

**of**Information

**"**or

**"**Point

**of**Interest

**"**or

**"**Pevis

**"**or

**"**Coffee Break ")

**which**is

**a**signal for

**all**players

**to**put down their cards

**,**while discussion takes place

**.**

__Any__instrument will reach

**a**

__point__where an increase in sample concentration will not result in an increase in

**the**reported absorbance

**,**because

**the**detector is simply responding

**to**

**the**stray light

**.**

__Any__traveller attempting

**to**pass into

**the**eastern regions

**of**Middle-earth would have

**to**cross

**the**Anduin at some

__point__along its long course

**(**unless

**one**passed through

**the**extreme north

**,**risking

**a**passage through

**the**Grey Mountains ).

According

**to****the**historian**of**science Norwood Russell Hanson**:**There is no bilaterally-symmetrical**,**nor excentrically-periodic curve used in**any**branch**of**astrophysics or observational astronomy**which**could not be smoothly plotted as**the**resultant motion**of****a**__point__turning within**a**constellation**of**epicycles**,**finite in number**,**revolving around**a**fixed deferent**.**__Any__path — periodic or not**,**closed or**open**— can be represented with an infinite number**of**epicycles**.**__Any__balance

**the**music maintained up

**to**

**that**

__point__

**,**however fragile

**,**is lost and so

**,**more than likely

**,**is

**the**listener

**.**

Any and x

:*

__Any__total order on**X**has exactly**one**equivalence class**,****X**itself**,**because__x__~ y for**all**__x__and y ;__Any__commutative monoid is endowed with its algebraic preordering ≤, defined

**by**

__x__≤ y if and only if there exists z such

**that**

__x__+ z

**=**y

**.**

__Any__statement

**of**

**the**form

**"**for

**any**number

__x__..."

**that**is true for

**the**reals is also true for

**the**hyperreals

**.**

__Any__preordered set

**(**P

**,**≤) forms

**a**small category

**,**where

**the**objects

**are**

**the**members

**of**P

**,**

**the**morphisms

**are**arrows pointing

**from**

__x__

**to**y when

__x__≤ y

**.**

__Any__monoid

**(**

**any**algebraic structure with

**a**single associative binary operation and an identity

**element**

**)**forms

**a**small category with

**a**single object

__x__

**.**

__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 >.

__Any__

**of**

**the**100 squares in

**the**superimposed 10

__x__10 grid can be accurately described using

**a**digit

**from**0-9

**(**with 0 0 being

**the**bottom left square and 9 9 being

**the**top right square ).

A weight on

**a**Lie algebra g over**a**field F is**a**linear map λ**:**g → F with λ**(**y )= 0 for**all**__x__**,**y in g**.**__Any__weight on**a**Lie algebra g vanishes on**the**derived algebra and hence descends**to****a**weight on**the**abelian Lie algebra g /.__Any__transformation

**of**

**the**plane leaving this pattern invariant can be decomposed into

**a**translation

**,**

**(**

__x__

**,**y

**)**→

**(**n +

__x__

**,**y ), optionally followed

**by**

**a**reflection in either

**the**horizontal axis

**,**

**(**

__x__

**,**y

**)**→

**(**

__x__,− y ), or

**the**vertical axis

**,**

**(**

__x__

**,**y

**)**→ (−

__x__

**,**y ), provided

**that**this axis is chosen through or midway between two dots

**,**or

**a**rotation

**by**180 °,

**(**

__x__

**,**y

**)**→ (−

__x__,− y

**)**

**(**ditto ).

Any and gives

*

__Any__expression formed using**any**combination**of****the**basic arithmetic operations and extraction**of**nth roots__gives__an algebraic number**.**__Any__accelerating electric charge

**,**and therefore

**any**changing electric current

**,**

__gives__

**rise**

**to**an electromagnetic wave

**that**propagates at very high speed outside

**the**surface

**of**

**the**conductor

**.**

__Any__second-countable

**space**is separable

**:**if is

**a**countable base

**,**choosing

**any**

__gives__

**a**countable dense subset

**.**

*

__Any__principal bundle with structure group G__gives__**a**groupoid**,**namely over M**,**where G acts on**the**pairs componentwise**.**__Any__smooth

**function**on

**a**symplectic manifold

__gives__

**rise**

**,**

**by**definition

**,**

**to**

**a**Hamiltonian vector field and

**the**set

**of**

**all**such form

**a**subalgebra

**of**

**the**Lie Algebra

**of**symplectic vector fields

**.**

__Any__ξ ∈

__gives__

**rise**

**to**

**a**canonical vertical vector field

**X**

**<**

**sub**

**>**ξ

**</**

**sub**

**>**

**by**taking

**the**derivative

**of**

**the**right action

**of**

**the**1-parameter subgroup

**of**H associated

**to**ξ

**.**

__Any__prime number

**p**

__gives__

**rise**

**to**an ideal pO

**<**

**sub**

**>**K

**</**

**sub**

**>**in

**the**ring

**of**integers O

**<**

**sub**

**>**K

**</**

**sub**

**>**

**of**

**a**quadratic field K

**.**

__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__surface

**that**intersects

**the**wire has current I passing through

**it**so Ampère's law

__gives__

**the**correct magnetic field

**.**

__Any__ring homomorphism A → B

__gives__

**a**map K

**<**

**sub**

**>**0

**</**

**sub**

**>(**A

**)**→ K

**<**

**sub**

**>**0

**</**

**sub**

**>(**B

**)**

**by**mapping

**(**

**the**class

**of**

**)**

**a**projective A-module M

**to**M ⊗<

**sub**

**>**A

**</**

**sub**

**>**B

**,**making K

**<**

**sub**

**>**0

**</**

**sub**

**>**

**a**covariant functor

**.**

:(

**1****)**__Any__person who manufactures**,**sells or hires or offers for sale or hire**,**or exposes or has in his possession for**the**purpose**of**sale or hire or lends or__gives__**to****any**other person —__Any__kind

**of**connection on

**a**manifold

__gives__

**rise**

**,**through its parallel transport maps

**,**

**to**some notion

**of**holonomy

**.**

__Any__skew semistandard tableau

**of**shape / with positive integer entries

__gives__

**rise**

**to**

**a**sequence

**of**partitions

**(**or Young diagrams ),

**by**starting with

**,**and taking for

**the**partition places further in

**the**sequence

**the**

**one**whose diagram is obtained

**from**

**that**

**of**

**by**adding

**all**

**the**boxes

**that**contain

**a**value ≤ in ; this partition eventually becomes equal

**to**

**.**

__Any__attempt

**to**drastically increase this range

**(**

**by**increasing

**the**angular extent

**of**

**the**true radius lobe nose region

**)**soon

__gives__

**rise**

**to**problems with excessive rates

**of**valve acceleration etc

**.**

__Any__nontrivial line arrangement on RP

**<**sup

**>**2

**</**sup

**>**defines

**a**graph in

**which**each face is bounded

**by**at least three edges

**,**and each edge bounds two faces ; so

**,**double counting

__gives__

**the**additional inequality F ≤ 2E / 3

**.**

Let now v and w be two vertices in G

**.**__Any__spanning tree contains precisely**one**simple path between v and w**.**Taking this path in**the**uniform spanning tree__gives__**a**random simple path**.**__Any__

**topological**

**space**

**X**

__gives__

**rise**

**to**

**a**category where

**the**objects

**are**

**the**

**points**

**of**

**X**and

**the**morphisms

**are**

**the**homotopy classes

**of**paths

**.**

In his letter

**,**Polding__gives__Wardell**a**completely free hand in**the**design**,**saying**"**__Any__plan**,****any**style**,**anything**that**is beautiful and grand**,****to****the**extent**of**our power**.**0.572 seconds.