(mathematics) The formation of quotients.

(grammar) Of an adverb: expressing how often, or how many times.

(arithmetic) The number resulting from the division of one number by another. / (arithmetic) The integer part of the result of such division.

plural of quotient

plural of quotient space

(topology and algebra) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.

(algebra) A field all of whose elements can be represented as ordered pairs each of whose components belong to a given integral domain, such that the second component is non-zero, and so that the additive operator is defined like so: (a,b)+(a',b')=(ab'+a'b,bb'), the multiplicative operator is defined coordinate-wise, the zero is (0,1), the unity is (1,1), the additive inverse of (a,b) is (-a,b), equivalence is defined like so: (a,b)≡(a',b') if and only if ab'=a'b, and multiplicative inverse of a non-zero–equivalent element (a,b) is (b,a).

(topology) A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.

(algebra, ring theory) For a given ring R and ideal I contained in R, another ring, denoted R / I, whose elements are the cosets of I in R.

plural of quotient ring