Page "Compact space" ¶ 83
from Wikipedia

## Some Related Sentences

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.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
Every contraction mapping is Lipschitz continuous and hence uniformly continuous ( for a Lipschitz continuous function, the constant k is no longer necessarily less than 1 ).
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 Lipschitz continuous map is uniformly continuous, and hence a fortiori continuous.
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 map
Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.
Every smooth ( or differentiable ) map φ: M → N between smooth ( or differentiable ) manifolds induces natural linear maps between the corresponding tangent spaces:
Every distinct map projection distorts in a distinct way.
Every inner automorphism is indeed an automorphism of the group G, i. e. it is a bijective map from G to G and it is a homomorphism ; meaning ( xy )< sup > a </ sup >
* Every constant map is a plot.
Every regular map of varieties is continuous in the Zariski topology.
Every real m-by-n matrix yields a linear map from R < sup > n </ sup > to R < sup > m </ sup >.
Every algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic map of C into J.
Every local homeomorphism is a continuous and open map.
Every covering map is a semicovering, but semicoverings satisfy the " 2 out of 3 " rule: given a composition of maps of spaces, if two of the maps are semicoverings, then so also is the third.
* Every bundle of Lie algebras over a smooth manifold defines a Lie algebroid where the Lie bracket is defined pointwise and the anchor map is equal to zero.
Every Möbius transformation is a bijective conformal map of the Riemann sphere to itself.
* The embedding theorem for Stein manifolds states the following: Every Stein manifold of complex dimension can be embedded into by a biholomorphic proper map.
Every issue of our periodical will therefore include one or more map supplements, and their design will guarantee a continuous and easily accessible supplement in easy-to-manage form with special regard for those who own Stielers Hand-Atlas, Berghaus ’ s Physical Atlas, and other map publications of the ( Perthes ) Institute.
Every map consists of numerous textured polygons carefully positioned in relation to one another.
Every summer, the town prepares for the one-week summer festival, " Finnsnes i Fest ", aiming to put Finnsnes on the map.
* Every map can be replaced by a cofibration via the mapping cylinder construction
* Every local diffeomorphism is also a local homeomorphism and therefore an open map.
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.
Every map has these two bases, but each map has a different pattern of fixed terrain features.

Every and from
Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.
Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.
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 pitch in the game brought forth a howl from the enraptured audience and every fly ball the visitors dropped ( and because their right fielder was still a little fuzzy from drink, they dropped many ) called forth yelps of derision.
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 book followed a different train of thought, from inspiration to solution, according to her autobiography.
Every time a speech sound is produced for a given phoneme, it will be slightly different from other utterances, even for the same speaker.
: Every non-empty set A contains an element B which is disjoint from A.
Every year both clubs play the " Klassieker " (" The Classic "), a derby match between the teams from the two largest cities of the Netherlands.
Four other hits from the album made the Pop top 20: " Every Heartbeat " ( No. 2 ), " That's What Love Is For " ( No. 7 ), " Good For Me " ( No. 8 ), and " I Will Remember You " ( No. 20 ).
* Revised Code of Washington 9. 12. 010: " Every person who brings on his or her own behalf, or instigates, incites, or encourages another to bring, any false suit at law or in equity in any court of this state, with intent thereby to distress or harass a defendant in the suit, or who serves or sends any paper or document purporting to be or resembling a judicial process, that is not in fact a judicial process, is guilty of a misdemeanor ; and in case the person offending is an attorney, he or she may, in addition thereto be disbarred from practicing law within this state.
Every year, the European Joint Conferences on Theory and Practice of Software ( ETAPS ) sponsors the International Conference on Compiler Construction ( CC ), with papers from both the academic and industrial sectors.
Every Halloween, Dabney House conducts the infamous " Millikan pumpkin-drop experiment " from the top of Millikan Library, the highest point on campus.
Every year many teams from all over Asia converge in Tokyo to compete.
Every argues that " the disparagement of myth in our own civilization " stems partly from objections to perceived idolatry, objections which intensified in the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance.
Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed.
In Norse mythology, Draupnir ( Old Norse " the dripper ") is a gold ring possessed by the god Odin with the ability to multiply itself: Every ninth night eight new rings ' drip ' from Draupnir, each one of the same size and weight as the original.
Every time a diode switches from on to off or vice versa, the configuration of the linear network changes.
* Every June, Ellensburg hosts Dachshunds on Parade, an event that draws Dachshund dog owners from all over the Northwest.
For example the words of " I'm a Man You Don't Meet Every Day " ( Roud 975 ) are known from a broadside in the Bodleian Library.
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.

0.325 seconds.