Vlastimil Pták introduced a modified form of this property after noting how the open mapping theorem of functional analysis critically relies on this property of the spaces to conclude that the image of the unit ball under a continuous linear operator contains a ball centered at the origin. Spaces that are metrizable, locally convex, and have this property are named for Maurice Fréchet (“FREH-shay”). A non-empty space with this property cannot be expressed as a countable union of nowhere dense subsets. (-5[1])A theorem due to Stefan Banach (“BAH-nokh”) states that a contraction mapping on a space with this property has a unique fixed point. Any metric space can be expanded to have this property by constructing a space whose elements are equivalence classes of sequences. Extending the rationals to a space with this property gives the reals. For 10 points, name this property that means every Cauchy (“KOH-shee”) sequence converges. ■END■ (0[1])