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Continuous function A function f from a topological space X to a topological space Y such that, for each open U ⊆ Y , the set f −1 (U ) is open in X. For functions on the real line, this is equivalent to requiring that, for any > 0, there exists a δ > 0 such that |f (x) − f (y)| < whenever |x − y| < δ. , a complete and complemented modular lattice L such that given any element x of L and any subset W of L which is well ordered with respect to the ordering in L, then x ∩ sup w = sup(a ∩ w), where w ∈ W .

See recursively enumerable. , at any step during the execution of the instructions, there must be at most one instruction that can be applied. This notion is intuitive for a corresponding formal mathematical notion. See computable, recursive. Eilenberg-Steenrod Axioms Let T be a category of pairs of topological spaces and continuous maps and let A denote the category of Abelian groups. ) A functor Hp : T → A for each integer p ≥ 0, whose value is denoted Hp (X, A). If f : (X, A) → (Y, B) is a continuous map, let (f∗ )p denote the induced map from Hp (X, A) to Hp (Y, B).

Division algorithm If a and b = 0 are in Z, there exist unique integers r so that a = bq + r and 0 ≤ r < b. A clever repeated application of the division algorithm, known as Euclid’s algorithm, leads to the computation of the greatest common divisor of the integers a and b. See Euclidean algorithm. 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.

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A Buddhist Chinese- Sanskrit Dictionary by Akira Hirakawa

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