By Catherine Cavagnaro, II, William T. Haight
Containing greater than 1,000 entries, the Dictionary of Classical and Theoretical arithmetic makes a speciality of mathematical phrases and definitions of severe value to training mathematicians and scientists. This single-source reference presents operating definitions, meanings of phrases, similar references, and an inventory of different phrases and definitions. The dictionary is one in every of 5 constituent works that make up the casebound CRC finished Dictionary of Mathematics.
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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. See covering transformation. In the special case where E is the universal cover of B, this group is isomorphic to the fundamental group of the space B.
Division algorithms hold in other rings, such as the polynomials with real coefficients. the dual bundle ξ ∗ of ξ has the projection divisor If a and b are elements of a ring and there exists an element c in that ring satisfying bc = a, then b (similarly, c) is a divisor of a. For example, in the ring of integers, 6 is a divisor of 24 since 6 × 4 = 24 (and 4, 6, and 24 are all integers), while 5 is not a divisor of 24 since there is no integer c so that 5c = 24. However, in the ring Z36 (the integers mod 36), 5 is a divisor of 24 since 5 × 12 = 24 in Z36 (alternatively, 5 × 12 ≡ 24 (mod 36)).
An important consequence of this is the Brouwer Fixed-Point Theorem: Every continuous map f : B n → B n has a fixed point. © 2001 by CRC Press LLC derived set The set of accumulation points of a subset A of a topological space X. The derived set of A is written A . The closure of A is then A ∪ A , and A is closed if and only if A ⊆ A. determined Let X be a subset of ωω . Associated with X is the game GX which is played by differential invariant two players A and B. The two players alternate choosing natural numbers a1 , b1 , a2 , b2 , .