quotient space


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quotient space

[′kwō·shənt ‚spās]
(mathematics)
The topological space Y which is the set of equivalence classes relative to some given equivalence relation on a given topological space X ; the topology of Y is canonically constructed from that of X. Also known as factor space.
References in periodicals archive ?
The quotient space theory and random theory are the use equivalent class state "granularity", described the concept with "granularity" again.
A binary classification of multilevels granulation searching algorithm, namely, establishing an efficient multigranulation binary classification searching model based on hierarchical quotient space structure, is proposed in this paper.
Godeaux surfaces with an involution over C were studied by Keum and Lee [9], and subsequently Calabri, Ciliberto, and Mendes Lopes [4] classified the possibilities for the quotient space of a Godeaux surface by its involution, proving that it is either rational or birational to an Enriques surface.
We recall that a partition [pi] of X is said to be a Hausdorff partition if the quotient space X/[pi] is Hausdorff.
We begin with a lemma which was given by Fatemeh Lael and Kourosh Nouruzi[2], by using the norm [parallel]x + <e>[parallel] = [parallel]x,e[parallel]/[parallel]e,e'[parallel] in the quotient space X/<e>.
n]) is a quotient space obtained from a topological sum ([X.
The Brownian map is described as a quotient space of the continuous random tree called the CRT, for an equivalence relation that is defined in terms of Brownian labels assigned to the vertices of the CRT (see Sections 3 and 4 below for a detailed discussion).
The theory, fuzzy set theory, rough set theory, a superset of the theory of quotient space and interval calculation, a branch of soft computing science (LI, 2005).
Let B(M, A) denote the quotient space T/ ~, and let p: T [right arrow] B(M, A) be the quotient map.
This extremely large and comprehensive handbook on granular computing traces this relatively new discipline's roots in artificial intelligence, interval computing and quotient space theory and explores the growing interest in this subject due to advances in bioinformatics, data mining, wireless technologies and e-commerce.
His topics include quotient spaces, the uniform boundedness principle, projections, the Fredholm alternative, symmetric linear operators, sesquilinear functional, and an operational calculus.
After a review of real numbers, sequences, and continuity for real-valued functions of one variable, the book covers continuity in metric and topological spaces, subspaces and product spaces, and the Hausdorff condition, as well as connected and compact spaces, sequential compactness, quotient spaces and surfaces, uniform convergence, and complete metric spaces.