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.