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Every and mapping
Every singleton is a terminal object, with the functions mapping all elements of the source sets to the single target element as morphisms.
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 year, the American Society for Photogrammetry and Remote Sensing ( ASPRS ) presents the Talbert Abrams Award to a person who makes an outstanding contribution to aerial photography and mapping.
Every measurable entity maps into a cardinal function but not every cardinal function is the result of the mapping of a measurable entity.
* Every map can be replaced by a cofibration via the mapping cylinder construction

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 single problem touched on thus far is related to good marketing planning.
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 man in every one of these houses is a Night Rider.
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 infinite game in which is a Borel subset of Baire space is determined.
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 root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
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 Lipschitz
* Every Lipschitz continuous map is uniformly continuous, and hence a fortiori continuous.
Every special uniformly continuous real-valued function defined on the metric space is uniformly approximable by means of Lipschitz functions.

Every and continuous
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.
* 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.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
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 space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every separable metric space is isometric to a subset of C (), the separable Banach space of continuous functions → R, with the supremum norm.
Every uniformly continuous function between metric spaces is continuous.
Every continuous function on a compact set is uniformly continuous.
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 continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
Every embedding is injective and continuous.
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.
* Every compact Hausdorff space of weight at most ( see Aleph number ) is the continuous image of ( this does not need the continuum hypothesis, but is less interesting in its absence ).
Every place south of the Antarctic Circle experiences a period of twenty-four hours ' continuous daylight at least once per year, and a period of twenty-four hours ' continuous night time at least once per year.

Every and hence
* 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 topological ring is a topological group ( with respect to addition ) and hence a uniform space in a natural manner.
Every finite-dimensional normed space is reflexive, simply because in this case, the space, its dual and bidual all have the same linear dimension, hence the linear injection J from the definition is bijective, by the rank-nullity theorem.
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 finite-dimensional simple algebra over C must be a matrix ring over C and hence every central simple algebra over C must be a matrix ring over C.
* T-carbon: Every carbon atom in diamond is replaced with a carbon tetrahedron ( hence ' T-carbon ').
Every perfect matching is maximum and hence maximal.
Every year a number of kloofers get injured or need rescue and hence kloofers need to take great care and preferably be accompanied by an experienced kloofer.
* Every substructure is the union of its finitely generated substructures ; hence Sub ( A ) is an algebraic lattice.
Every city and town accessible to those sounds hence became vulnerable to attack.
# Every plurality, being a combination of units, presupposes an original unity ; hence, even those that assume a plurality of gods must logically admit the prior existence of a Divine Unity — a Neoplatonic argument borrowed by Baḥya from the Brothers of Purity.
Contraries cannot both be true, although they can both be false, and hence their contradictories are both true ( for example, both, ' Every man is honest ,' and ' No man is honest ,' are false.
Every human mind inherits a complement of species-specific “ elementary ideas ” ( Elementargedanken ), and hence the minds of all people, regardless of their race or culture, operate in the same way.
# Every elementary substructure of a model of a theory T also satisfies T ; hence it is a submodel.
Previously a daily segment, Underbelly didn't appear as often in the rotation ( hence Maddow's inclination to add " Every day ... or so " to her introduction of the segment ).
The Commission Report quotes Max Weber, Every bureaucracy seeks to increase the superiority of the professionally informed by keeping their knowledge and intentions secret ... Bureaucracy naturally welcomes a poorly informed and hence a powerless parliament — at least insofar as ignorance somehow agrees with the bureaucracy ’ s interests.
Every Friday night, the counselors organize " an event so fun that it is necessary and sufficient ," hence the name " mandatory fun.
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.

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