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We extend the property (N) introduced by Jameson for closed convex cones to the normal property for a nite collection of convex sets in a Hilbert space. Variations of the normal property, such as the weak normal property and the uniform normal property, are also introduced. A dual form of the normal property is derived. When applied to closed convex cones,(More)
Bauschke, Borwein, and Lewis have stated a trichotomy theorem [4, Theorem 5.7.16] that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem. In this note, we show that although one of the errors is critical, the theorem itself is correct. We give a(More)
An elementary proof of the Stone-Weierstrass theorem is given. In this note we give an elementary proof of the Stone-Weierstrass theorem. The proof depends only on the definitions of compactness ("each open cover has a finite subcover") and continuity ("the inVerse images of open sets are open"), two simple consequences of these definitions (i.e. "a closed(More)