Download e-book for iPad: An A-Z of English Grammar and Usage by Geoffrey N. Leech

By Geoffrey N. Leech

Книга рассчитана на все группы пользователей, так как описывает базовые принципы английской грамматики. В книге в простой форме описываются все базовые правила языка, кроме того для всех грамматическим терминов даны пояснения и описания так, что даже новичку будет несложно разобраться в правилах языка. Дополнительным плюсом является использование общераспространенных тем, которые обычно не встречаются в других книгах: как извиниться или поблагодарить в той или иной ситуации, какие существуют нюансы.

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The Eilenberg-Steenrod axioms are the following five axioms: Exactness Axiom. The sequence · · · → Hp (A) (i∗ )p (π∗ )p Hp (X) Hp (X, A) → → elementarily equivalent structures ∂p Hp−1 (A) → . . → is exact, where i : A → X and π : X → (X, A) are the inclusion maps. Homotopy Axiom. If h and k are homotopic, then (h∗ )p = (k∗ )p for each p. Excision Axiom. Given (X, A), let U be an open subset of X such that U¯ ⊂ IntA. If (X \ U, A \ U ) is in A, then the inclusion (X \ U, A \ U ) → (X, A) induces an isomorphism Hp (X \ U, A \ U ) Hp (X, A) .

L = α∈Ord Lα . contact element In the Euclidean plane R2 , an ordered pair (p, ) consisting of a point p and a line containing the point p. More generally, a contact element in a smooth n-dimensional manifold M is a pair (p, H ) consisting of a point p in M and an n − 1-dimensional plane H in the tangent space at p. The contact elements in M form a (2n−1)-dimensional manifold which has a special structure on it called a contact structure. contact form A one-form ω on a smooth (2n + 1)-dimensional manifold M such that ω ∧ (dω)n = 0 everywhere on M.

For example, the map p(t) = (cos t, sin t) is a covering map from R to the unit circle. covering space A topological space X is a covering space of Y if there is a covering map p : X → Y . See covering map. For example, R is a covering space of the unit circle via p(t) = (cos t, sin t). covering transformation A map φ : E −→ E such that p ◦ φ = φ, where p : E −→ B is a covering map of an arcwise connected, locally arcwise connected space B. See covering map. covering transformation group The group of covering transformations φ : E −→ E, under composition.

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An A-Z of English Grammar and Usage by Geoffrey N. Leech


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