# 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.
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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 [1] in terms of quotient maps and cozero elements and equivalently reformulated in [6] in terms of sublocales and continuous real functions.

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