This is an incredibly useful notion, which we will use from time to time to simplify other tasks. Definition Quotient topology by an equivalence relation. 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 quotient space is a quotient object in some category of spaces, such as Top (of topological spaces), or Loc (of locales), etc. A quotient is the result of a division problem. a quotient vector space. Learn more. quotient definition: 1. a particular degree or amount of something: 2. the result of dividing one number by another 3â¦. quotient synonyms, quotient pronunciation, quotient translation, English dictionary definition of quotient. 15.30. The quotient space is already endowed with a vector space structure by the construction of the previous section. 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. dividend divide divisor quotient. 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].. a topological space whose elements are the equivalence classes of a given topological space with a specified equivalence relation. V is the vector space and U is the subspace of V. We define a natural equivalence relation on V by setting v â¼ w if v â w â U. Let Y be another topological space and let f â¦ Definition of quotient space Suppose X is a topological space, and suppose â¦ Find definitions for: quo'tient space" Pronunciation: â Math. Definition. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange Quotient definition, the result of division; the number of times one quantity is contained in another. Quotient. See more. Definition: Quotient Space 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. quotient space: A space obtained from another by

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