Google says they are aware of the need for

constant map updates, which helps users to better navigate and facilitates travel planning.

Notice that if e is a constant map with range {a} [subset or equal to] X, then [I.sub.e] = [I.sub.a], where

Notice that if e is a constant map with range {a} [subset or equal to] Y, then [I.sub.e] = [I.sub.a] and

Because X is an ENR, there is a smaller open neighbourhood [V.sub.0] [??] V of [x.sub.0] inside V such that the inclusion [V.sub.0] [right arrow] V is homotopic, through a homotopy inside V that fixes [x.sub.0], to the constant map at [x.sub.0].

(For the degree zero case d = 0, we can also take f to be the constant map at [[e.sub.0]].

Let p be an arbitrary value in U and F be in [N.sub.[partial derivative]U]([bar.U], C) and be the constant map F(x) = p for x in [bar.U].

By Lemma 7, the constant map [T.sub.0](x) = [psi](t) for x [member of] [bar.U] is essential.

is homotopic to a constant map which sends [DELTA] ([f.sup.-1] (Q < q)) to [c.sup.q] for some [c.sup.q] [member of] [DELTA] ([f.sup.-1] ((q))).

As in the proof of Theorem 1.1 in [10], it follows that there exists a homotopy from the inclusion map [DELTA]([f.sup.-1] ([Q.sub.<q])) [right arrow] [DELTA]([f.sup.-1] ((q))) to the constant map which sends [DELTA]([f.sup.-1]( [Q.sub.<q])) to [c.sup.q] [member of] [DELTA]([f.sup.-1] ((q))).

* (Normalization) If cis a

constant map, then i(c; M) = 1

(i) [[mu].sup.T.sub.[alpha]] is a maximal fuzzy extension of [mu]u if and only if [mu] is a

constant map.

Using the above terminology the authors show in [IK12a] that [SL.sub.n](O(X)) is boundedly elementary generated when X is a finite dimensional reduced Stein space with the property that all holomorphic mappings from X to [SL.sub.n] (C) are null-homotopic, that is homotopic (through a family of continuous maps) to a

constant map. This result is an application of the Oka-Grauert-Gromov-h-principle in Complex Analysis.