* 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 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 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.

Every form is the delimitation of a surface by another one ; it possesses an inner content, the effect it produces on one who looks at it attentively.

Every aspect of the store is mapped out and attention is paid to colour, wording and even surface texture.

Every gland is formed by an ingrowth from an epithelial surface.

Every antiseptic, however good, is more or less toxic and irritating to a wounded surface ; as a result, in surgery, the antiseptic method has been replaced by aseptic method, which is preventative in nature and relies on keeping free from the invasion of bacteria rather than destroying them when present.

Every Riemann surface is a two-dimensional real analytic manifold ( i. e., a surface ), but it contains more structure ( specifically a complex structure ) which is needed for the unambiguous definition of holomorphic functions.

Every Riemann surface is the quotient of a free, proper and holomorphic action of a discrete group on its universal covering and this universal covering is holomorphically isomorphic ( one also says: " conformally equivalent ") to one of the following:

# Every Riemannian metric on a Riemann surface is Kähler, since the condition for ω to be closed is trivial in 2 ( real ) dimensions.

# Every K3 surface is Kähler ( by a theorem of Y .- T. Siu ).

Every smooth surface S has a unique affine plane tangent to it at each point.

Every now and then, the surface water sloshes back across the ocean, bringing warm water temperatures along the eastern coasts of the pacific.

Every such black body emits from its surface with a spectral radiance that Kirchhoff labeled ( for specific intensity, the traditional name for spectral radiance ).

Every 17 years, Brood X cicadas tunnel en masse to the surface of the ground, lay eggs, and then die off in several weeks.

Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.

Every conic surface is ruled and developable.

Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.

Every vehicle function that changes direction or speed relies on friction between the tires and the road surface.

Every single object or point is dwarfed ; the valley of the Hudson is only a wrinkle in the earth's surface.

Every surface of the vaulted ceiling is occupied with preserved fishes, stuffed mammals and curious shells, with a stuffed crocodile suspended in the centre.

Every integer 2g ' 2g matrix with < sup >*</ sup > arises as the Seifert matrix of a knot with genus g Seifert surface.

Every morning before sunrise, the floor of the owners house, or where ever it may be, is cleaned with water and the muddy floor is swept well for an even surface.

Every hyperbolic Riemann surface has a non-trivial fundamental group.

According to Dale E. Dawkins, AMC's vice-president, " Every square inch of inner surface on exterior body panels is galvanized on our Spirit, Concord, and Eagle models.

Every particular finite line, surface, or solid which may possibly be the object of our thought is an idea existing only in the mind, and consequently each part of it must be perceived.