\begin{align} \quad \| (x_{n_2} + y_2) - (x_{n_3} + y_3) \| \leq \| (x_{n_2} - x_{n_3}) + M \| + \frac{1}{4} < \frac{1}{4} + \frac{1}{4} = \frac{1}{2} \end{align} quotient definition: 1. a particular degree or amount of something: 2. the result of dividing one number by another 3â¦. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of proper division). General (4 matching dictionaries) quotient-space, quotient space: Wiktionary [home, info] quotient space: Infoplease Dictionary [home, info] If X is a topological space and A is a set and if : â is a surjective map, then there exist exactly one topology on A relative to which f is a quotient map; it is called the quotient topology induced by f . A quotient is the result of a division problem. A continuous map between topological spaces is termed a quotient map if it is surjective, and if a set in the range space is open iff its inverse image is open in the domain space.. A topological space is sequential if and only if it is a quotient of a metric space. In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced / Ë k w oÊ Ê Én t /) is a quantity produced by the division of two numbers. Definition Quotient topology by an equivalence relation. Jump to: General, Art, Business, Computing, Medicine, Miscellaneous, Religion, Science, Slang, Sports, Tech, Phrases We found one dictionary with English definitions that includes the word quotient-space: Click on the first link on a line below to go directly to a page where "quotient-space" is defined. Definition of quotient noun in Oxford Advanced Learner's Dictionary. a topological space whose elements are the equivalence classes of a given topological space with a specified equivalence relation. âQuotient spaceâ covers a lot of ground. Let be topological spaces and be continuous maps. a quotient vector space. quotient space - definition and meaning This can be visualized as gluing these points together in a single point, forming a quotient space.There is, however, no reason to expect such quotient spaces to be manifolds. (The Universal Property of the Quotient Topology) Let X be a topological space and let Ëbe an equivalence relation on X. Endow the set X=Ëwith the quotient topology and let Ë: X!X=Ëbe the canonical surjection. In other words, it is the solution to the question "how many times does a number (the divisor) go into another (the dividend).A division problem can be structured in a number of different ways, as shown below. Definition Symbol-free definition. The quotient space of a topological space and an equivalence relation on is the set of equivalence classes of points in (under the equivalence relation ) together with the following topology given to subsets of : a subset of is called open iff is open in .Quotient spaces are also called factor spaces. Definition: Quotient Space Let (X, Ï X) be a topological space, and let ~ be an equivalence relation on X.The quotient set, Y = X / ~ is the set of equivalence classes of elements of X.As usual, the equivalence class of x â X is denoted [x].. quotient space: A space obtained from another by

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