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* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.
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Every and totally
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
Every non-empty totally ordered set is directed.
* Every totally ordered set with the order topology is Tychonoff.
* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
* Every totally ordered set is a distributive lattice with max as join and min as meet.
Every November the Reebok Stadium hosts Kidz up North which is one of the largest free UK exhibitions totally dedicated to children with disabilities and special needs, their parents, carers and professionals who work with them.
Every subset of a totally bounded space is a totally bounded set ; but even if a space is not totally bounded, some of its subsets still will be.
* Every compact set is totally bounded, whenever the concept is defined.
* Every totally bounded metric space is bounded.
Every compact metric space is totally bounded.
Every and ordered
** Antichain principle: Every partially ordered set has a maximal antichain.
* Every cofinal subset of a partially ordered set must contain all maximal elements of that set.
Every subfield of an ordered field is also an ordered field in the inherited order.
Every ordered field contains an ordered subfield that is isomorphic to the rational numbers.
Every ordered field is a formally real field.
Every subfield of an ordered field is also an ordered field ( inheriting the induced ordering ).
Every ordered field can be embedded into the surreal numbers.
Every ordered field is a formally real field, i. e., 0 cannot be written as a sum of nonzero squares.
* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.
Every relatively atomic partially ordered set with a least element is atomic.
Every ordered basis lives in one equivalence class or another.
Every time she entered, song typical of the Brazilian northeast would play, stopping only when ordered by Cirene herself.
Every partially ordered set is cofinal in itself.
Every and set
: Every set has a choice function.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** Well-ordering theorem: Every set can be well-ordered.
* 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 non-empty set A contains an element B which is disjoint from A.
* 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.
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 corporation, whether financial or union, as well as every division of the administration, were set up as branches of the party, the CEOs, Union leaders, and division directors being sworn-in as section presidents of the party.
Every DNS zone must be assigned a set of authoritative name servers that are installed in NS records in the parent zone, and should be installed ( to be authoritative records ) as self-referential NS records on the authoritative name servers.
Group actions / representations: Every group G can be considered as a category with a single object whose morphisms are the elements of G. A functor from G to Set is then nothing but a group action of G on a particular set, i. e. a G-set.
# " Personality " Argument: this argument is based on a quote from Hegel: " Every man has the right to turn his will upon a thing or make the thing an object of his will, that is to say, to set aside the mere thing and recreate it as his own ".
Every atom across this plane has an individual set of emission cones .</ p > < p > Drawing the billions of overlapping cones is impossible, so this is a simplified diagram showing the extents of all the emission cones combined.
* Every singleton set
Every processor or processor family has its own machine code instruction set.
Every set is a class, no matter which foundation is chosen.
* Every preorder can be given a topology, the Alexandrov topology ; and indeed, every preorder on a set is in one-to-one correspondence with an Alexandrov topology on that set.
Every binary relation R on a set S can be extended to a preorder on S by taking the transitive closure and reflexive closure, R < sup >+=</ sup >.
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