Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

# Every infinite subset of X has a complete accumulation point.

Every compact metric space is complete, though complete spaces need not be compact.

Every soul has to follow the path, as explained by the Jinas and revived by the tirthankaras, to attain complete liberation or nirvana.

*( BCT1 ) Every complete metric space is a Baire space.

Every time Emperor Wen sent generals out on battles, he required them to follow the complete battle plans that he had drafted, and even the dates for battles needed approval from the emperor.

Every use of a bank machine, payment by credit card, use of a phone card, call from home, checked out library book, rented video, or otherwise complete recorded transaction generates an electronic record.

Every logical calculation, from the simplest to the most complex, must complete in one clock cycle.

Every time he is thrown out of the house, he is shown wearing the same shirt although he does not always wear it when he is thrown out ( the producers never shot a second sequence with Jazz being thrown out of the house, only adjusting the original scene for time purposes ; an exception is in the episode " Community Action ", where Jazz was thrown out along with a lifesize cardboard cut-out of Bill Cosby, complete with a blooper showing Jeff Townes reshooting his flying off the house several times ).

Every two years, before migration, the adult Common Crane undergoes a complete moult, remaining flightless for six weeks, until the new feathers grow.

*( BCT1 ) Every complete metric space is a Baire space.

Every complete musical piece projects a single key and ultimately a single stufe ( the tonic ).

Every student who intents to pass the matura is required to complete four exams:

Every projective variety is complete, but not vice versa.

" Every opening phase of a Canadian operation was a complete success and the staff works a mathematical masterpiece … the Canadian Army never followed up their opening successes to reach a complete victory.

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 5 years, each Commission conducts a complete review of all constituencies in its part of the United Kingdom.

Every month, a employer must file a complete IR348 Employer monthly schedule with the IRD, stating the income and deductions of each employee.

Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.

Every Skolem theory is model complete, i. e. every substructure of a model is an elementary substructure.

Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to.

Every year on the third Saturday in September, German-Americans celebrate the Annual Steuben Parade on Fifth Avenue and an Oktoberfest-style beer fest complete with food and live music in Central Park.

Every connected graph is an expander ; however, different connected graphs have different expansion parameters.

Every individual is connected with the rest of the world, and the universe is fashioned for universal harmony.

Every aspect of life, every word, plant, animal and ritual was connected to the power and authority of the gods.

* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

* Every connected graph with only countably many vertices admits a normal spanning tree.

Every aspect of life, every word, plant, animal and ritual was connected to the power and authority of the gods.

Every device connected to one of its ports can send packets to any of the others.

The generalized Poincaré conjecture states that Every simply connected, closed n-manifold is homeomorphic to the n-sphere.

Every closed 3-manifold has a prime decomposition: this means it is the connected sum of prime three-manifolds ( this decomposition is essentially unique except for a small problem in the case of non-orientable manifolds ).

Every part of it, including the blue and white colors ( see below ), the cross, as well as the stripe arrangement can be connected to very old historical elements ; however it is difficult to establish " continuity ", especially as there is no record of the exact reasoning behind its official adoption in early 1822.

Every Eulerian orientation of a connected graph is a strong orientation, an orientation that makes the resulting directed graph strongly connected.

Every maximal outerplanar graph satisfies a stronger condition than Hamiltonicity: it is node pancyclic, meaning that for every vertex v and every k in the range from three to the number of vertices in the graph, there is a length-k cycle containing v. A cycle of this length may be found by repeatedly removing a triangle that is connected to the rest of the graph by a single edge, such that the removed vertex is not v, until the outer face of the remaining graph has length k.

Every broadcasting company has members and the number of members gives them a status that is connected to the number of hours of broadcasting.

Every vertex of an-dimensional box is connected to edges.

Every graph ( that is connected and not a tree ) has multiple spanning trees, so we once again have an example where the problem itself allows multiple possible outcomes, and the algorithm chosen can arrive at any one of them, but will never arrive at something else.

This flat may be identified with the partition of the vertices of into the connected components of the subgraph formed by: Every set of edges having the same closure as gives rise to the same partition of the vertices, and may be recovered from the partition of the vertices, as it consists of the edges whose endpoints both belong to the same set in the partition.

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

* Every external device connected to the Freebox player is available to that device only but the devices connected to the Freebox Server are available to every Freebox player connected.

Every extra foot of cord increases the electrical resistance, which decreases the power the cord can deliver to connected devices.

Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere.

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