* Every uniform isomorphism and isometric isomorphism is a homeomorphism.

Every local homeomorphism is a continuous and open map.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

Every homeomorphism is open, closed, and continuous.

* Every local diffeomorphism is also a local homeomorphism and therefore an open map.

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 CW-complex possesses a Postnikov tower, that is, it is homotopy equivalent to an iterated fibration with fibers the Eilenberg – MacLane spaces.

* Every homotopy equivalence between two Hilbert manifolds is homotopic to a diffeomorphism.

Every element of is a member of the equivalence class.

Every two equivalence classes and are either equal or disjoint.

Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes ( or congruence classes ) for the relation.

Every adjunction 〈 F, G, ε, η 〉 extends an equivalence of certain subcategories.

Every equivalence or duality of abelian categories is exact.

Every commodity is listed separately, and there is never any sign of equivalence between one unit and another.

Every ordered basis lives in one equivalence class or another.

Every year, there are growing numbers of regional, national and international wrestling fan conventions, where fans can meet and converse with wrestlers and each other.

Every simple module is indecomposable, but the converse is in general not true.

Every regular space is locally regular, but the converse is not true.

Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.

* Every free abelian group is torsion-free, but the converse is not true, as is shown by the additive group of the rational numbers Q.

* 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.

It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.

Every dcpo is an ω-cpo, since every ω-chain is a directed set, but the converse is not true.

In mathematics, an integer-valued polynomial ( also known as a numerical polynomial ) P ( t ) is a polynomial whose value P ( n ) is an integer for every integer n. Every polynomial with integer coefficients is integer-valued, but the converse is not true.

Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub ( A ) for some algebra A.

Every rational variety, including the projective spaces, is rationally connected, but the converse is false.

Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree.

Every absolutely convergent series is unconditionally convergent, but the converse implication does not hold in general.