Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

Every regular ordinal is the initial ordinal of a cardinal.

* Every regular language is context-free because it can be described by a context-free grammar.

* Every metric space is Tychonoff ; every pseudometric space is completely regular.

* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.

* Every topological group is completely regular.

* Every normal regular space is completely regular, and every normal Hausdorff space is Tychonoff.

* Every subspace of a completely regular or Tychonoff space has the same property.

* Every Borel set E is outer regular:

* Every open set E is inner regular:

Every regular space is locally regular, but the converse is not true.

Every such space is regular.

Nordau saw in Jewish Emancipation the result of ' a regular equation: Every man is born with certain rights ; the Jews are human beings, consequently the Jews are born to own the rights of man.

Every such regular cover is a principal G-bundle, where G = Aut ( p ) is considered as a discrete topological group.

Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.

Every fourth year when the games were also held, the festival was known as the " Great Panathenaia ," and was 3 or 4 days longer than the regular festival.

“ Every three months ( after regular cleaning ) the wheels should be coated with petroleum jelly .”

Every US President since Roosevelt has delivered a regular address.

Every polyhedron, regular and irregular, convex and concave, has a dihedral angle at every edge.

Every extremal monomorphism is regular.

Every extremal epimorphism is regular.

* 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 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 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 Lipschitz continuous map is uniformly continuous, and hence a fortiori continuous.

Every distinct map projection distorts in a distinct way.

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 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 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.