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Some Related Sentences
Every and finite

** Tukey's lemma:
Every non-empty collection
of finite character has
a maximal element with respect
to inclusion
.

#
Every open cover
of A has
a finite subcover
.
* Countably compact:
Every countable open cover has
a finite subcover
.

#
Every finite and contingent being has
a cause
.
Every finite simple group is isomorphic
to one
of the following groups:

Hilbert's example: "
the assertion that either there are
only finitely many prime numbers or there are infinitely many " ( quoted
in Davis 2000: 97 );
and Brouwer's: "
Every mathematical species is either
finite or infinite
.
Every finite tree structure has
a member that has no superior
.
Every rational number / has two closely related expressions
as a finite continued fraction
, whose coefficients
can be determined by applying
the Euclidean algorithm
to.
* Every finite tree with n vertices
, with
, has at least two terminal vertices ( leaves ).
Every finite group
of exponent n with m generators is
a homomorphic image
of B < sub > 0 </ sub >( m
, n ).
Every known Sierpinski number k has
a small covering set
, a finite set
of primes with at least one dividing k · 2 < sup > n </ sup >+ 1 for each n > 0
.
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 oriented prime closed 3-manifold
can be cut along tori
, so that
the interior
of each
of the resulting manifolds has
a geometric structure with
finite volume
.
Every finite or bounded interval
of the real numbers that contains an infinite number
of points must have at least one point
of accumulation
.
Every field
of either type
can be realized
as the field
of fractions
of a Dedekind domain
in which every non-zero ideal is
of finite index
.
Every process involving charged particles emits infinitely many coherent photons
of infinite wavelength
, and the amplitude for emitting any
finite number
of photons is zero
.
Every finite group has
a composition series
, but not
every infinite group has one
.
* Every finite or cofinite subset
of the natural numbers is computable
.
* Every subset
of may
be covered by
a finite set
of positive orthants
, whose apexes all belong
to
* Every finite subextension
of F / k is separable
.
Every finite ordinal ( natural number ) is initial
, but most infinite ordinals are not initial
.
* Every finite-dimensional central simple algebra over
a finite field must
be a matrix ring over that field
.
* Every commutative semisimple ring must
be a finite direct product
of fields
.
Every and topological
* 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 topological group is completely regular
.
Every group
can be trivially made into
a topological group by considering it with
the discrete topology ; such groups are called discrete groups
.
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 topological ring is
a topological group ( with respect
to addition )
and hence
a uniform
space in a natural manner
.
Every local field is isomorphic (
as a topological field )
to one
of the following:
* Every non-empty Baire
space is
of second category
in itself
, and every intersection
of countably many dense open subsets
of X is non-empty
, but
the converse
of neither
of these is true
, as is shown by
the topological disjoint sum
of the rationals
and the unit interval 1
.
Every directed acyclic graph has
a topological ordering
, an ordering
of the vertices such that
the starting endpoint
of every edge occurs earlier
in the ordering than
the ending endpoint
of the edge
.
Every Boolean algebra
can be obtained
in this way from
a suitable
topological space: see Stone's representation theorem for Boolean algebras
.
Every such regular cover is
a principal G-bundle
, where G = Aut ( p ) is considered
as a discrete
topological group
.
Every Boolean algebra is
a Heyting algebra when
a → b is defined
as usual
as ¬
a ∨ b
, as is
every complete distributive lattice when
a → b is taken
to be the supremum
of the set
of all c for
which a ∧ c
≤ b
. The open sets
of a topological space form
a complete distributive lattice
and hence
a Heyting algebra
.
* Every constant function between
topological spaces is continuous
.
Every topological group is an H-space ; however
, in the general case
, as compared
to a topological group
, H-spaces may lack associativity
and inverses
.
Every interior algebra
can be represented
as a topological field
of sets with
its interior
and closure operators corresponding
to those
of the topological space.
Every separable
topological space is ccc
.
Every metric
space which is ccc is also separable
, but
in general
a ccc
topological space need not
be separable
.
Every locally compact group
which is second-countable is metrizable
as a topological group ( i
. e
. can be given
a left-invariant metric compatible with
the topology )
and complete
.
0.215 seconds.