Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

* 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.

* In any ring R, a maximal ideal is an ideal M that is maximal in the set of all proper ideals of R, i. e. M is contained in exactly 2 ideals of R, namely M itself and the entire ring R. Every maximal ideal is in fact prime.

Every year, thousands of cases of plague are still reported to the World Health Organization, although, with proper treatment, the prognosis for victims is now much better.

( DD1 ) Every nonzero proper ideal factors into primes.

Every proper rotation is the composition of two reflections, a special case of the Cartan – Dieudonné theorem.

Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ).

Every element in O ( 1, 3 ) can be written as the semidirect product of a proper, orthochronous transformation and an element of the discrete group

# Every man shall be called fairly in turn by the list on board of prizes, because over and above their proper share, they are allowed a shift of clothes.

Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one of the following:

Every elder in the Church is or should be an apostle ; that is, as a minister of the Lord and as a recipient of personal revelation from the Holy Ghost, every elder has the call to bear witness of the truth on all proper occasions.

: Every vessel must at all times maintain a proper look-out by sight ( day shape or lights by eyes or visual aids ) and hearing ( sound signal or Marine VHF radio ) as well as by all available means ( e. g., Radar, Automatic Radar Plotting Aid ( ARPA ), Automatic Identification System ( AIS ), GMDSS ...) in order to make a full assessment of the situation and risk of collision.

Every proper coloring and cocoloring of a graph are also subcolorings, so the subchromatic number of any graph is at most equal to the cochromatic number, which is at most equal to the chromatic number.

Every infinitesimal region of space time may have its own proper time that corresponds to the gravitational time dilation there, where electromagnetic radiation and matter may be equally affected, since they are made of the same essence ( as shown in many tests involving the famous equation E = mc < sup > 2 </ sup >).

* The embedding theorem for Stein manifolds states the following: Every Stein manifold of complex dimension can be embedded into by a biholomorphic proper map.

He summed up his philosophy by saying: " Every Plant has fitness and must be placed in its proper surroundings so as to bring out its full beauty.

Every second weekend he would stay at his father's condo in Montreal proper.

Every living thing was related in a branching pedigree, not ascending a Lamarckian ladder, and this pedigree was the proper basis for classification.

Every ornament is at a proper distance, and not one too large, but all delicate and new, with more freedom and variety than Greek ornaments ; and, though probably borrowed from the Hotel de Condé and other new Palaces, not one that is not rather classic than French.

: Every person who under color of any statute, ordinance, regulation, custom, or usage, of any State or Territory or the District of Columbia, subjects, or causes to be subjected, any citizen of the United States or other person within the jurisdiction thereof to the deprivation of any rights, privileges, or immunities secured by the Constitution and laws, shall be liable to the party injured in an action at law, Suit in equity, or other proper proceeding for redress, except that in any action brought against a judicial officer for an act or omission taken in such officer's judicial capacity, injunctive relief shall not be granted unless a declaratory decree was violated or declaratory relief was unavailable.

Every barangay has a Catholic Chapel, which are maintained by the Lay Ministers Of St. Bartholomew Parish Church-Located in the town proper of San Manuel.

Every barangay ( village ) has its own Roman Catholic chapel aside from the parish church in the town proper.

Every psyker is in danger of going insane or being possessed by a daemon if he does not have the proper training and strength of will.

* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.

* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem

Every subgroup of a topological group is itself a topological group when given the subspace topology.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

Every subgroup of a free abelian group is itself free abelian, which is important for the description of a general abelian group as a cokernel of a homomorphism between free abelian groups.

Every group of prime order is cyclic, since Lagrange's theorem implies that the cyclic subgroup generated by

Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.

* Every subgroup and quotient group of a locally cyclic group is locally cyclic.

* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.

Every compact Lie group G of dimension > 0 has a subgroup isomorphic to the circle group.

* Every ( closed ) subgroup of an amenable goup is amenable.

Recall that a subsemigroup G of a semigroup S is a subgroup of S ( also called sometimes a group in S ) if there exists an idempotent e such that G is a group with identity element e. A semigroup S is group-bound if some power of each element of S lies in some subgroup of S. Every finite semigroup is group-bound, but a group-bound semigroup might be infinite.

Every subgroup is organized around a set of brothers, each of whom is often married to a group of sisters.

Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.

Every closed subgroup of a locally compact group is locally compact.

Every quasinormal subgroup is a modular subgroup, that is, a modular element in the lattice of subgroups.

Every quasinormal subgroup is conjugate permutable.

Every normal subgroup is quasinormal, because, in fact, a normal subgroup commutes

Every group has itself ( the improper subgroup ) and the trivial subgroup as two of its fully characteristic subgroups.