Quotient metric space synonyms, Quotient metric space pronunciation, Quotient metric space translation, English dictionary definition of Quotient metric space. Quotient definition is - the number resulting from the division of one number by another. Quotient space definition, a topological space whose elements are the equivalence classes of a given topological space with a specified equivalence relation. In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given space.The points to be identified are specified by an equivalence relation. quotient space: A space obtained from another by identification of points that are equivalent to one another in some equivalence relation. Let Y be another topological space and let f … This is an incredibly useful notion, which we will use from time to time to simplify other tasks. 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 When we have a group G acting on a space X, there is a “natural” quotient space. 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. Noun 1. metric space - a set of points such that for every pair of points there is a nonnegative real number called their distance that is … If is a metric map between metric spaces (that is, for all x, y) satisfying f(x)=f(y) whenever then the induced function , given by , is a metric map . quotient space - definition and meaning We define a norm on X/M by. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more. A topological space is sequential if and only if it is a quotient of a metric space. How to use quotient in a sentence. Shimura's book "Introduction to the arithmetic theory of automorphic functions" explains in a detailed way that $\Gamma\backslash\mathcal{H}$ is a Riemann surface. Theorem 5.1. Let be topological spaces and be continuous maps. quotient space: Meaning and Definition of. Definition: Quotient Space In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero. Definition: Quotient Topology . You can have quotient spaces in set theory, group theory, field theory, linear algebra, topology, and others. In topology and related areas of mathematics, a quotient space (also called an identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given space.The points to be identified are specified by an equivalence relation. dividend divide divisor quotient. In Section 2 we recall all necessary definitions, and in Section 3 we consider two axioms, denoted by M and G, each not derivable from S4 and the other one, and for each of them we give necessary and sufficient conditions under which it is valid in a quotient space of a finite CW-complex, a particular point topological space, and an excluded point topological space. A quotient space is a quotient object in some category of spaces, such as Top (of topological spaces), or Loc (of locales), etc. Quotient. a topological space whose elements are the equivalence classes of a given topological space with a specified equivalence relation. 15.30. For each x ∈ X, let Gx = {g(x) | g ∈ G}. The quotient metric d is characterized by the following universal property. is termed a quotient map if it is sujective and if is open iff is open in . Learn more. “Quotient space” covers a lot of ground. Definition.Let (X, S) be a topological space, let Q be a set, and let π : X → Q be a surjective mapping.The resulting quotient topology (or identification topology) on Q is defined to be We found 7 dictionaries with English definitions that include the word quotient space: Click on the first link on a line below to go directly to a page where "quotient space" is defined. 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). In arithmetic, a quotient (from Latin: quotiens "how many times", pronounced / ˈ k w oʊ ʃ ən t /) is a quantity produced by the division of two numbers. Math. quotient-space definition: Noun 1. attributive form of quotient spacequotient-space mapNoun (plural quotient spaces) 2. $\begingroup$ From the answers it should be clear that it is sometimes better to read Chapter 1 first, and only then Chapter 2.