# quotient space

(redirected from Quotient map)

## 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.
Mentioned in ?
References in periodicals archive ?
3] [right arrow] P(V) can be identified with the quotient map [P.
2) f is a quotient map, if U open in Y whenever [f.
Let f : X [right arrow] Y be a quotient map from a Frechet space X onto Y.
Let [Pi] : X [approaches] X/Y denote the quotient map.
Consider the quotient map [Mathematical Expression Omitted].
Firstly, let us recall a simple lemma about factorization of linear maps beetwen locally convex spaces by the quotient map (see e.
Let T : X [right arrow] Z be a linear map beetwen locally convex spaces, Y be a closed subspace of X and q : X [right arrow] X/Y be the quotient map.
It is clear because f is a quotient map from a metric space onto X .
Note that the quotient map f obtained by identifying two distinct points a, b in X is a density preserving dual map.
The natural quotient map obtained by identifying H and K to distinct points is an atom in DP(X, A).
Here the first map is the inclusion, the second map is the quotient map, and the composed map is [[mu].
The notion of complete separation in pointfree topology was first introduced in  in terms of quotient maps and cozero elements and equivalently reformulated in  in terms of sublocales and continuous real functions.

Site: Follow: Share:
Open / Close