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Page "Bounded set (topological vector space)" ¶ 10
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Every and relatively
Every two years in Aremark there is a relatively large festival: Elgfestivalen ( elk festival ).
( Every datum is relatively oriented with respect to different portions of the geoid by the astro-geodetic methods already described.
Every H * is very special in structure: it is pure-injective ( also called algebraically compact ), which says more or less that solving equations in H * is relatively straightforward.
Every relatively atomic partially ordered set with a least element is atomic.
Every finite poset is relatively atomic, and every finite poset with 0 is atomic.
Every Friday evening, MISU hosts a well-attended social function in the Mariner's Lounge ; with relatively affordable beverages and live entertainment, commonly in the form of popular Parson's Pond breakdancer Paul Payne.
They wrote and recorded a new batch of songs relatively quickly and Every Kind of Light was released in June 2005 ; its songs " Love Comes " and " I Guess You're Right " are included as sample music tracks in the release of Microsoft's Windows Vista operating system.

Every and compact
* 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 compact metric space is separable.
* 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.
* Sequentially compact: Every sequence has a convergent subsequence.
* Countably compact: Every countable open cover has a finite subcover.
* Limit point compact: Every infinite subset has an accumulation point.
Every compact metric space is complete, though complete spaces need not be compact.
Every entire function can be represented as a power series that converges uniformly on compact sets.
* Every compact metric space ( or metrizable space ) is separable.
* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
Every Tychonoff cube is compact Hausdorff as a consequence of Tychonoff's theorem.
Every continuous function on a compact set is uniformly continuous.
Every compact Hausdorff space is also locally compact, and many examples of compact spaces may be found in the article compact space.
* 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 ).
*( BCT2 ) Every locally compact Hausdorff space is a Baire space.
Every group has a presentation, and in fact many different presentations ; a presentation is often the most compact way of describing the structure of the group.
*( BCT2 ) Every locally compact Hausdorff space is a Baire space.

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.
** 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.
** Antichain principle: Every partially ordered set has a maximal antichain.
* 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 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 cofinal subset of a partially ordered set must contain all maximal elements of that set.
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 non-empty totally ordered set is directed.
* 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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