3] [right arrow] P(V) can be identified with the quotient map
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.