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Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two$\sigma$-compact open projections. It is proved that there is a continuous pathof unitaries in ${\tilde A}$ which connects open sub-projections of $p$ whichis compactly contained in $p$ to those in $q.$ It is also shown that everyHilbert module is projective in the category whose morphisms are bounded modulemaps with adjoints. A discussion of projective Hilbert modules (whose morphismsare bounded module maps) is also given.

Cuntz semigroups of C*-algebras of stable rank one and projective Hilbert modules