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Some Related Sentences
Every and compact
* Every topological
space X
is a dense subspace
of a
compact space having
at most one point more than X
, by
the Alexandroff one-point compactification.
* Every compact metric
space is separable.
* 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.
* Sequentially
compact:
Every sequence has a convergent subsequence.
* Countably
compact:
Every countable open cover has a finite subcover.
* Limit point
compact:
Every infinite subset has an accumulation point.
Every compact metric
space is complete
, though complete spaces
need not be
compact.
Every entire function can be represented as a power series that converges uniformly on
compact sets.
* Every compact metric
space ( or metrizable
space ) is separable.
* Every locally
compact regular
space is completely regular
, and therefore every locally
compact Hausdorff space is Tychonoff.
Every Tychonoff cube
is compact Hausdorff as a consequence
of Tychonoff's theorem.
Every continuous function on a
compact set
is uniformly
continuous.
Every compact Hausdorff space is also locally
compact, and many examples
of compact spaces may be found
in the article
compact space.

*( BCT2
) Every locally
compact Hausdorff space is a Baire
space.
Every group has a presentation
, and
in fact many different presentations ; a presentation
is often
the most compact way
of describing
the structure
of the group.

*( BCT2
) Every locally
compact Hausdorff space is a Baire
space.
Every H
* is very special
in structure: it
is pure-injective
( also called algebraically
compact ), which says more or
less that solving equations
in H
* is relatively straightforward.
Every and Hausdorff
* Every normal regular
space is completely regular
, and every normal
Hausdorff space is Tychonoff.
Every finite-dimensional
Hausdorff topological vector
space is reflexive
, because J
is bijective by linear algebra
, and because there
is a unique
Hausdorff vector
space topology on a finite dimensional vector
space.
* Every CW complex
is compactly generated
Hausdorff.
Every and space

**
Every vector
space has a basis.

**
Every infinite game
in which
is a Borel subset
of Baire
space is determined.

**
Every Tychonoff
space has a Stone – Čech compactification.
* Theorem
Every reflexive normed
space is a Banach
space.
Every Hilbert
space X
is a Banach
space because
, by definition
, a Hilbert
space is complete with respect to
the norm associated with
its inner product
, where a norm and an inner product are said to be associated if for all x ∈ X.
* Pseudocompact:
Every real-valued
continuous function on
the space is bounded.
Every subset A
of the vector
space is contained within a smallest convex set
( called
the convex hull
of A ), namely
the intersection
of all convex sets containing A.
Every point
in three-dimensional Euclidean
space is determined by three coordinates.
Every node on
the Freenet network contributes storage
space to hold files
, and bandwidth that it uses to route requests from
its peers.
Every space filling curve hits some points multiple times
, and
does not have a
continuous inverse.
* 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 vector
space has a basis
, and all bases
of a vector
space have
the same
number of elements
, called
the dimension
of the vector
space.
Every normed vector
space V sits as a dense subspace inside a Banach
space ;
this Banach
space is essentially uniquely defined by V and
is called
the completion
of V.
Every and weight
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.

In Norse mythology
, Draupnir
( Old Norse "
the dripper ")
is a gold ring possessed by
the god Odin with
the ability to multiply itself:
Every ninth night eight new rings ' drip ' from Draupnir
, each one
of the same size and
weight as
the original.
Every day
, records were taken including what he did
at what time
, weight, and anything else
of note.
Every ship
, submarine
, and dirigible must be designed to displace a
weight of fluid equal to
its own
weight.
Every effort was made to keep
the weight of the vehicle under 20 tons.
Every wire was able to be traced from origin to destination with software and
the weight of the cable interconnecting cabinets was automatically calculated by an RCA 501 machine language program named " signal path " written by Robert Goerss
, computing facility director.
Every piece
of equipment
is evaluated for a balance
of utility versus
weight.
Every step
is with full
weight transfer.
Every weight is a
number between λ and − λ which differs from them by an integer and has multiplicity one.
Every time a variable
in grade
, traction
, or wheel slip occurs
, the computer will adjust
the pressure
in these cylinders to maintain sufficient adhesion
, by varying
the weight on
the drive axles.
Every square inch
of a giant bone had to support 10 times
the weight borne by a square inch
of human bone.
Every codeword
in a Type III code has Hamming
weight divisible by 3.
Every step
is with full
weight transfer.
Every hour
, Lindbergh switches fuel tanks to keep
the weight load balanced.
0.406 seconds.