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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.

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## Some Related Sentences

Every and map

*

__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__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__smooth (

**or**differentiable )

__map__φ: M → N between smooth (

**or**differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:

__Every__inner automorphism

**is**indeed

**an**automorphism of the group G

**,**i

**.**e

**.**it

**is**a bijective

__map__from G to G

**and**it

**is**a homomorphism

**;**meaning ( xy )< sup > a </ sup >

__Every__algebraic curve C of genus g ≥ 1

**is**associated with

**an**abelian variety J of dimension g

**,**by means of

**an**analytic

__map__of C into J

**.**

__Every__covering

__map__

**is**a semicovering

**,**but semicoverings satisfy the " 2 out of 3 " rule: given a composition of maps of spaces

**,**if two of the maps

**are**semicoverings

**,**then so

**also**

**is**the third

**.**

*

__Every__bundle of Lie algebras over a smooth manifold defines a Lie algebroid where the Lie bracket**is**defined pointwise**and**the anchor__map__**is**equal to zero**.**
* The

**embedding**theorem for Stein manifolds states the following:__Every__Stein manifold of complex dimension can be embedded into by a biholomorphic proper__map__**.**__Every__issue of our periodical will therefore include one

**or**more

__map__supplements

**,**

**and**their design will guarantee a

**continuous**

**and**easily accessible supplement in easy-to-manage form with special regard for those who own Stielers Hand-Atlas

**,**Berghaus ’ s Physical Atlas

**,**

**and**other

__map__publications of the ( Perthes ) Institute

**.**

__Every__summer

**,**the town prepares for the one-week summer festival

**,**" Finnsnes i Fest ", aiming to put Finnsnes on the

__map__

**.**

__Every__element x of G gives rise to a tensor-preserving self-conjugate natural transformation via multiplication by x on each representation

**,**

**and**hence one has a

__map__

**.**

Every and is

__Every__legislator from Brasstown Bald to Folkston

__is__going to have his every vote subjected to the closest scrutiny as a test of his political allegiances

**,**not his convictions

**.**

__Every__detail in his interpretation has been beautifully thought out

**,**

**and**of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation (

**an**obvious indication

**that**he

__is__playing with Viennese musicians )

**,**

**and**the gossamer shading throughout

**.**

__Every__taxpayer

__is__well aware of the vast size of our annual defense budget

**and**most of our readers

**also**realize

**that**a large portion of these expenditures go for military electronics

**.**

__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__dream

**,**

**and**this

__is__true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought

**,**

__is__a psychic phenomenon for

**which**no explanation

__is__available

**.**

__Every__library borrower

**,**

**or**at least those whose taste goes beyond the five-cent fiction rentals

**,**knows what it

__is__to hear the librarian say apologetically

**,**`` I'm sorry

**,**but we don't have

**that**book

**.**

__Every__community

**,**if it

__is__alive has a spirit

**,**

**and**

**that**spirit

__is__the center of its unity

**and**identity

**.**

The restricted principle "

__Every__partially ordered set has a maximal totally ordered subset "__is__**also**equivalent to AC over ZF**.**__Every__natural-born citizen of a foreign state who

__is__

**also**

**an**American citizen

**and**every natural-born American citizen who

__is__a citizen of a foreign land owes a double allegiance

**,**one to the United States

**,**

**and**one to his homeland ( in the event of

**an**immigrant becoming a citizen of the US ),

**or**to his adopted land ( in the event of

**an**emigrant natural born citizen of the US becoming a citizen of another nation ).

__Every__line of written text

__is__a mere reflection of references from any of a multitude of traditions

**,**

**or**

**,**as Barthes puts it

**,**" the text

__is__a tissue of quotations drawn from the innumerable centres of culture "; it

__is__never original

**.**

__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__lattice element of the structure

__is__in its proper place

**,**whether it

__is__a single atom

**or**a molecular grouping

**.**

Every and injective

__Every__morphism in a concrete category whose underlying function

**is**

__injective__

**is**a monomorphism

**;**in other words

**,**if morphisms

**are**actually functions between sets

**,**then any morphism

**which**

**is**a one-to-one function will necessarily be a monomorphism in the categorical sense

**.**

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